1.4 rewriting equations and formulas
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This document provides instructions for rewriting equations and formulas. It discusses rewriting equations with more than one variable by substituting values and then solving for the remaining variable. Common formulas are also restructured by solving for a specified variable through steps like multiplication, division, addition and subtraction. Worked examples demonstrate solving equations for variables like y, h, and b1.
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2.5 notes
The document discusses applying the distributive property to simplify algebraic expressions. It provides examples of distributing positive and negative coefficients over terms with variables and constants. Key parts of expressions like terms, coefficients, and constant terms are defined. Examples show identifying these parts and simplifying expressions using the distributive property and combining like terms. Practice problems at the end ask the reader to simplify expressions.
Simplifying algebraic expressions
1. The document provides instruction on simplifying algebraic expressions. It gives examples of identifying like terms and combining like terms by adding or subtracting coefficients.
2. Examples are provided to simplify expressions and write expressions for perimeter of triangles. Students are asked to justify steps using properties of algebra.
3. A quiz assesses identifying like terms, simplifying expressions, and writing expressions for perimeters of figures.
Algebra 2 Section 1-1
The document provides examples and explanations for solving linear equations. It begins by defining key vocabulary like open sentence, equation, and solution. It then shows how to translate between verbal and algebraic expressions. Various properties of equality like reflexive, symmetric, and transitive properties are explained. Finally, it demonstrates solving linear equations by isolating the variable using the inverse operations property of equality. Examples include solving equations with variables on both sides and checking solutions.
Simplifying algebraic expression
The document discusses an algebra lesson that reviewed combining like terms to simplify expressions and solve equations, including identifying like terms, using the distributive property, and solving one-step equations by combining like terms. Students are assigned IXL practice skills related to adding, subtracting, and multiplying linear expressions and combining like terms. MAP testing and no live classes the following week are also mentioned.
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This document provides examples and explanations for combining like terms in algebraic expressions. It includes examples of combining like terms with one variable, two variables, and using the distributive property to simplify expressions. The examples are followed by a short quiz with 5 problems involving combining like terms and simplifying expressions.
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This document provides an overview of simplifying algebraic expressions. It discusses algebraic expressions and examples. The key skills covered are using the distributive property to simplify expressions involving grouping symbols and combining like terms. Examples are provided to demonstrate simplifying expressions using these skills along with evaluating expressions by substituting values for variables.
polynomials class 9th maths presentation
This document contains a summary of key concepts in polynomials including:
1) Definitions of terms like variable, term, coefficient, degree, constant and zero polynomials.
2) The Remainder Theorem and how it relates the remainder of polynomial division to the factor theorem.
3) The Factor Theorem and how it can be used to determine if a polynomial is a factor of another.
4) Examples of factoring polynomials and using the Factor Theorem.
5) A list of 15 common algebraic identities involving polynomials.
Algebraic expressions
1. An algebraic expression is a combination of numbers, variables, and operation symbols. It can be classified as a monomial, binomial, or trinomial based on the number of terms.
2. Like terms contain the same variables raised to the same powers, while unlike terms do not. Multiplication of algebraic expressions follows rules such as the product of like signs being positive and unlike signs being negative.
3. There are special product identities for multiplying binomials and factoring algebraic expressions through grouping and finding greatest common factors. Division of algebraic expressions also follows rules regarding the signs of the quotient.
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The document discusses applying the distributive property to simplify algebraic expressions. It provides examples of distributing positive and negative coefficients over terms with variables and constants. Key parts of expressions like terms, coefficients, and constant terms are defined. Examples show identifying these parts and simplifying expressions using the distributive property and combining like terms. Practice problems at the end ask the reader to simplify expressions.
Simplifying algebraic expressions
1. The document provides instruction on simplifying algebraic expressions. It gives examples of identifying like terms and combining like terms by adding or subtracting coefficients.
2. Examples are provided to simplify expressions and write expressions for perimeter of triangles. Students are asked to justify steps using properties of algebra.
3. A quiz assesses identifying like terms, simplifying expressions, and writing expressions for perimeters of figures.
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The document provides examples and explanations for solving linear equations. It begins by defining key vocabulary like open sentence, equation, and solution. It then shows how to translate between verbal and algebraic expressions. Various properties of equality like reflexive, symmetric, and transitive properties are explained. Finally, it demonstrates solving linear equations by isolating the variable using the inverse operations property of equality. Examples include solving equations with variables on both sides and checking solutions.
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The document discusses an algebra lesson that reviewed combining like terms to simplify expressions and solve equations, including identifying like terms, using the distributive property, and solving one-step equations by combining like terms. Students are assigned IXL practice skills related to adding, subtracting, and multiplying linear expressions and combining like terms. MAP testing and no live classes the following week are also mentioned.
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This document provides examples and explanations for combining like terms in algebraic expressions. It includes examples of combining like terms with one variable, two variables, and using the distributive property to simplify expressions. The examples are followed by a short quiz with 5 problems involving combining like terms and simplifying expressions.
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This document provides an overview of simplifying algebraic expressions. It discusses algebraic expressions and examples. The key skills covered are using the distributive property to simplify expressions involving grouping symbols and combining like terms. Examples are provided to demonstrate simplifying expressions using these skills along with evaluating expressions by substituting values for variables.
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This document contains a summary of key concepts in polynomials including:
1) Definitions of terms like variable, term, coefficient, degree, constant and zero polynomials.
2) The Remainder Theorem and how it relates the remainder of polynomial division to the factor theorem.
3) The Factor Theorem and how it can be used to determine if a polynomial is a factor of another.
4) Examples of factoring polynomials and using the Factor Theorem.
5) A list of 15 common algebraic identities involving polynomials.
Algebraic expressions
1. An algebraic expression is a combination of numbers, variables, and operation symbols. It can be classified as a monomial, binomial, or trinomial based on the number of terms.
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3. There are special product identities for multiplying binomials and factoring algebraic expressions through grouping and finding greatest common factors. Division of algebraic expressions also follows rules regarding the signs of the quotient.
5.3 solving abs value equations
Absolute value equations can have two solutions, as they are equivalent to two separate equations where the absolute value is equal to the number or its negative. To solve absolute value equations, they are rewritten as two separate equations and then solved, with the answer written with both possible solutions separated by "or". More complex absolute value equations may require isolating the term inside the absolute value before splitting into two equations.
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1. The document discusses combining like terms using the distributive property.
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The document provides 4 ordered pairs as solutions to an equation: (5, 0); (4, 1); (1, 2); and (2, 3). It shows the steps of subtracting 3 from both sides of the equation, factoring the resulting expression as (a-3)(b+1)=2, and using a table to find the values of a and b that satisfy the factors and solutions.
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The document provides the solutions (5, 0), (4, 1), (1, 2), and (2, 3) to an equation. It shows the steps to subtract 3 from both sides of the equation ab + a - 3b - 3 = 5 - 3 and then factor the expression as (a - 3)(b + 1) = 2. A table is used to find the values of a and b that satisfy the factored equation and match the given solutions.
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The document provides 4 coordinate pairs as solutions to an equation: (5, 0); (4, 1); (1, 2); and (2, 3). It describes subtracting 3 from both sides of the equation to get (a-3)(b+1)=2, then using a table to find the values of a and b that satisfy the factors and solutions.
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A polynomial is an algebraic expression involving variables and constants that is formed using addition, subtraction, and multiplication, but not division. The degree of a polynomial refers to the highest power of the variable. Polynomials can be classified based on their number of terms as monomials (one term), binomials (two terms), or trinomials (three terms). They can also be classified based on degree as constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), or of higher degrees. The number of zeros of a polynomial is equal to its degree.
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- Discussing the history of polynomial notation pioneered by Descartes.
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- Outlining common uses of polynomials in mathematics, science, and other fields.
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The document discusses algebraic expressions and their components such as variables, coefficients, terms, and different types of expressions including monomials, binomials, and polynomials. It explains how to identify the variables, coefficients, and terms that make up an expression. Examples are provided to illustrate monomials containing one term, binomials containing two terms, and polynomials that can contain any number of terms.
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The document discusses how to solve simple and compound inequalities. It explains that solving inequalities follows the same process as solving equations, but requires paying attention to the inequality sign and graphing the solution set. It provides examples of solving different types of inequalities, such as those with addition, subtraction, multiplication, and division, noting that the inequality sign may need to be reversed when multiplying or dividing by a negative number.
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The document discusses how to graph and write systems of linear inequalities. It explains how to graph systems by determining whether lines should be dotted or solid based on the inequality symbols, and whether shading should be above or below lines based on 'y >' or 'y <'. It also explains how to write the system of inequalities given a graph by writing equations for each line and changing the equations to inequalities based on whether lines are dotted or solid and whether shading is above or below lines. Examples of these processes are provided.
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1. The document discusses absolute value functions of the form y = a|x - h| + k, where a ≠ 0.
2. It explains how to find the vertex (h, k) and line of symmetry x = h of an absolute value function graph.
3. It also describes how the graph opens up or down depending on whether a is positive or negative, and how the width compares to y = |x| depending on the value of |a|.
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5.3 solving abs value equations
Absolute value equations can have two solutions, as they are equivalent to two separate equations where the absolute value is equal to the number or its negative. To solve absolute value equations, they are rewritten as two separate equations and then solved, with the answer written with both possible solutions separated by "or". More complex absolute value equations may require isolating the term inside the absolute value before splitting into two equations.
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1. The document discusses combining like terms using the distributive property.
2. Like terms are terms that contain the same variables raised to the same power, while unlike terms do not.
3. To combine like terms, add the coefficients and keep the variables and powers the same.
Potw answer
The document provides 4 ordered pairs as solutions to an equation: (5, 0); (4, 1); (1, 2); and (2, 3). It shows the steps of subtracting 3 from both sides of the equation, factoring the resulting expression as (a-3)(b+1)=2, and using a table to find the values of a and b that satisfy the factors and solutions.
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The document defines exponents and provides examples of multiplying and combining like terms with exponents. It explains that to multiply terms, you multiply the coefficients and add the exponents of like terms. It provides examples of multiplying, combining, and dividing like terms with variables and exponents.
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2. The coordinates of a point on the graph of y=g(x) are (-3,5), so the coordinates of a point on the graph of y=h(-x) are (3,5).
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This document provides an overview of polynomials, including:
- Defining polynomials as expressions involving variables and coefficients using addition, subtraction, multiplication, and exponents.
- Discussing the history of polynomial notation pioneered by Descartes.
- Explaining the different types of polynomials like monomials, binomials, and trinomials.
- Outlining common uses of polynomials in mathematics, science, and other fields.
- Describing how to find the degree of a polynomial and graph polynomial functions.
- Explaining arithmetic operations like addition, subtraction, and division that can be performed on polynomials.
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This document contains formulas and examples for key algebraic concepts like like terms, coefficients, perimeter of rectangles and triangles, and area of rectangles and triangles. It also provides warm-up problems involving translating sentences to algebraic expressions and equations, and simplifying expressions. Finally, it outlines the topics and key concepts that will be covered on Test #1: simplifying expressions by combining like terms, solving one- and two-step equations, and translating sentences into algebraic representations.
Addition and subtraction of rational expression
To add or subtract fractions with unlike denominators:
1. Find the least common denominator (LCD), which contains all prime factors of each denominator raised to the highest power.
2. Convert the fractions to equivalent fractions with the LCD as the denominator.
3. Perform the addition or subtraction on the numerators and write the sum or difference over the common denominator.
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Solving literal equations involves finding the value of a variable in terms of other variables or constants. Examples of solutions to literal equations include x = 3y - a, y = 4 + x/r, and solving equations such as 3x - 4y = 7, dx - 2y = 3z, y = mx + b, or by + 2 = c/3 for the variable on one side of the equal sign.
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The document discusses algebraic expressions and their components such as variables, coefficients, terms, and different types of expressions including monomials, binomials, and polynomials. It explains how to identify the variables, coefficients, and terms that make up an expression. Examples are provided to illustrate monomials containing one term, binomials containing two terms, and polynomials that can contain any number of terms.
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This document provides an introduction to sequences through examples and definitions. Some key points:
- A sequence is a list of numbers in a given order, with each number called a term. The position of a term is its index.
- Examples of sequences include {2, 4, 6, 8,...} where the general term is an=2n, and {1/n} where the terms approach 0 as n increases.
- The order of terms is important to a sequence. Transforming the order results in a different sequence.
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This document provides an overview of key topics in mathematics including real numbers, prime factorization, rational and irrational numbers, and properties of the highest common factor (HCF) and lowest common multiple (LCM). Some key points covered include:
- The fundamental theorem of arithmetic which states that every composite number can be uniquely factored into prime numbers.
- Examples of factorizing numbers into their prime factors and using this to find the HCF and LCM of pairs of numbers.
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3.2 a solving systems algebraically
Here are the steps to solve this system of linear equations using the elimination method:
1) Line up the equations:
-4x - 8y = 16
6x + 12y = -24
2) Add a multiple of one equation to the other to eliminate x:
-4x - 8y = 16
6x + 12y = -24
Add -1.5 times the top equation to the bottom:
-4x - 8y = 16
0 - 3y = -40
3) Solve for y:
-3y = -40
y = 13
4) Substitute y = 13 back into either original equation to find x:
-4x
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53 multiplication and division of rational expressions
The document discusses multiplication and division of rational expressions. It presents the multiplication rule for rational expressions, which states that the product of two rational expressions is equal to the product of the tops divided by the product of the bottoms. Examples are provided to demonstrate simplifying rational expression products by factoring and canceling like terms.
4 multiplication and division of rational expressions
The document discusses multiplication and division of rational expressions. It presents the multiplication rule for rational expressions, which states that the product of two rational expressions is equal to the product of the top expressions divided by the product of the bottom expressions. Examples are provided to demonstrate simplifying rational expression products by factoring and canceling like terms.
Solving quadratic equations[1]
The document discusses various methods for solving quadratic equations: factoring, using square roots, and completing the square. It provides examples of using each method to solve equations arising from applications like finding the dimensions of a rectangle given its area. Sample problems are worked through step-by-step to find the solutions or roots of quadratic equations.
Solving quadratic equations
The document discusses various methods for solving quadratic equations: factoring, using square roots, and completing the square. It provides examples of using each method to solve equations as well as word problems involving quadratic equations. Factoring involves writing the quadratic as a product of two binomials and setting each factor equal to 0. Using square roots involves taking the square root of both sides of the equation to isolate the variable. Completing the square rewrites the equation by adding or subtracting terms to put it in the form (x+a)2=b and then taking the square root of both sides.
13 multiplication and division of rational expressions
The document discusses multiplication and division of rational expressions. It presents the multiplication rule for rational expressions as the product of the numerators over the product of the denominators. It provides an example of simplifying a rational expression by factoring the top and bottom and canceling like terms. It then gives another example with two parts, simplifying and expanding the answers of rational expression operations.
10.7
Here are the steps to solve the quadratic equations using the quadratic formula:
1) Write the equation in standard form: ax^2 + bx + c = 0
2) Identify the coefficients a, b, c
3) Plug the coefficients into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
4) Simplify the solution
The quadratic formula can be used to find the roots (solutions) of any quadratic equation in standard form. Other solution methods like factoring or completing the square may also work for certain equations.
Quadratic Function Presentation
The document defines and explains key concepts regarding quadratic functions including:
- The three common forms of quadratic functions: general, vertex, and factored form
- How to find the x-intercepts, y-intercept, and vertex of a quadratic function
- Methods for solving quadratic equations including factoring, completing the square, and the quadratic formula
- How to graph quadratic functions by identifying intercepts and the vertex
8 inequalities and sign charts x
The document discusses using sign charts to solve polynomial and rational inequalities. It provides examples of solving inequalities by setting one side equal to zero, factoring the expression, drawing the sign chart, and determining the solutions from the regions with the appropriate signs. Specifically, it works through examples of solving x^2 - 3x > 4, 2x^2 - x^3/(x^2 - 2x + 1) < 0, and (x - 2)/(2/(x - 1)) < 3.
Notes 3-2
The document discusses graph translations. It defines a translation as moving each point (x,y) on a graph to a new location (x+h, y+k) using horizontal and vertical magnitudes h and k. Examples show finding the rule for a translation based on a point mapping, translating points between graphs, and rewriting equations in vertex form to identify translations between parabolas. The key aspects are that translations shift graphs in the xy-plane using h and k values and the graph-translation theorem allows identifying translations by replacing x with x-h and y with y-k in equations.
Lesson 3 Operation on Functions
The Sum of Two Functions
The Difference of Two functions
The Product of Two Functions
The Quotient of Two Functions
The Product of A constant and a Function
Expresiones Algebraicas, Factorizaciòn y Radicaciòn
The document outlines an accounting training program taken by Claudimar Cañizalez. It covers the following topics in Unit 1:
1) Addition, subtraction, and evaluation of algebraic expressions
2) Multiplication and division of algebraic expressions
3) Factorization using factoring techniques like common factors, difference of squares, and quadratic formula.
Exercises are provided to demonstrate each technique.
2.5 apply the distributive property day 1
The document discusses the distributive property in algebra. It defines terms, like terms, and constant terms. It explains that the distributive property allows a number or variable outside a set of parentheses to be distributed to each term inside. Examples show using the distributive property to expand expressions like (a + b)(c), and to combine like terms. It provides mental math examples of using the distributive property to calculate total costs. Students are assigned problems applying the distributive property, with instructions to show the steps and use of the property from start to finish.
11.2
The document defines rational expressions as expressions that can be written as a ratio of two polynomials where the denominator is not 0. It provides examples of finding excluded values, which make the expression undefined, by setting the denominator equal to 0. It also discusses simplifying rational expressions by dividing out common factors in the numerator and denominator and putting them in simplest form. Examples are provided of factoring, dividing out monomials, recognizing opposites, and simplifying a rational model.
Similar to 1.4 rewriting equations and formulas (20)
3 multiplication and division of rational expressions x
3 multiplication and division of rational expressions x
53 multiplication and division of rational expressions
53 multiplication and division of rational expressions
4 multiplication and division of rational expressions
4 multiplication and division of rational expressions
13 multiplication and division of rational expressions
13 multiplication and division of rational expressions
Expresiones Algebraicas, Factorizaciòn y Radicaciòn
Expresiones Algebraicas, Factorizaciòn y Radicaciòn
More from fthrower
3.3 a solving systems of inequalities
1. Systems of linear inequalities can be solved by graphing the inequalities on a coordinate plane.
2. Each inequality is written in slope-intercept form (y=mx+b) and graphed as either a solid or dotted line.
3. The region representing the solution of the system is found by shading the area of overlap between the graphs based on whether each inequality represents "above or below" the line.
3.3 solving systems of inequalities
The document discusses solving systems of linear inequalities by graphing the inequalities on a coordinate plane. It explains that linear inequalities should be written in slope-intercept form and the corresponding lines should be drawn as dotted or solid based on the inequality symbols. It also notes that the solution region includes points not on the lines and instructs the reader to shade above or below lines depending on the inequality. An example problem demonstrates these steps to find the region satisfying two inequalities.
3.2 solving systems algebraically
Here are the steps to solve this system of equations using elimination:
1) Line up the equations:
-4x - 8y = 16
6x + 12y = -24
2) Multiply the top equation by -3:
12x + 24y = -48
6x + 12y = -24
3) Add the equations to eliminate y:
18x = -72
4) Divide both sides by 18:
x = -4
5) Substitute x=-4 into either original equation to find y:
-4(-4) - 8y = 16
16 - 8y = 16
-8y = 0
y = 0
So
3.1 b solving systems graphically
This document provides instructions for students to solve systems of linear equations by graphing. Students are asked to write equations in slope-intercept form when possible, use slope and y-intercept to determine the number of solutions (one, many, or no solutions), and name each system based on its number of solutions. The document assigns textbook problems #35-52 for practice and is dated for Friday, October 7th.
3.1 a solving systems graphically
This document discusses how to graph and solve systems of linear equations in two variables by determining whether the system has one solution, many solutions, or no solution. It explains that a consistent system has a solution, an inconsistent system has no solution, an independent system has one solution, and a dependent system has infinitely many solutions. It also notes that a system will have one solution if the lines cross once, no solution if the lines are parallel, and infinitely many solutions if the lines are the same.
3.4 a linear programming
The document discusses using linear programming to find the maximum and minimum values of an objective function given certain constraints. It provides an example of finding the minimum and maximum values of the function f(x,y)=3x-2y when constrained by y≥2, 1≤x≤5, and y≤x+3. The values are found by graphing the inequalities to determine the vertices and substituting the vertices into the objective function.
2.8 b absolute value functions
The document provides instructions for graphing and writing equations for absolute value functions. It discusses key aspects like the vertex, line of symmetry, slope, and general form of the equation. Examples are provided to demonstrate how to graph an absolute value function given its equation, and how to write the equation of an absolute value function given its graph by finding the vertex and another point.
2.8 a absolute value functions
1. The document discusses absolute value functions and how to graph and write equations for them.
2. It explains that the graph of an absolute value function is V-shaped and defines the vertex and line of symmetry.
3. Examples are provided to demonstrate how to graph an absolute value function by finding the vertex and slope and plotting points, and how to write the equation of an absolute value function given its graph.
2.6 graphing linear inequalities
This document discusses graphing linear inequalities. It has two objectives: 1) determining if an ordered pair is a solution to an inequality, and 2) graphing linear inequalities in one and two variables.
2.5 a correlation & best fitting lines
The document discusses finding the line of best fit for a data set using linear regression. It explains that the line of best fit should have approximately the same number of points above and below the line. It also describes how the slope of the line indicates whether the correlation is positive, negative, or relatively no correlation. Finally, it introduces the correlation coefficient r as a measure of the strength of correlation, with values closer to 1 or -1 indicating a stronger correlation.
2.4 writing equations of lines
1) This document discusses writing linear equations in slope-intercept form (y=mx+b) given different information: the slope (m) and y-intercept (b), a graph, the slope and a point, or two points.
2) It provides examples of writing equations of lines given: the slope and y-intercept, a graph, the slope and a point, two points, or the x- and y-intercepts.
3) The key steps are to identify the slope (m) and y-intercept (b) from the information provided, then substitute those values into the slope-intercept form equation to write the linear equation.
2.3 linear equations
The document discusses linear equations and how to graph them. It defines linear equations as having variables with exponents of 1 that are added or subtracted. It explains how to identify the slope and y-intercept of a linear equation in slope-intercept form (y=mx+b) in order to graph it as a line on the coordinate plane. Key steps include solving for y and identifying the slope (m) and y-intercept (b). Examples are provided to demonstrate finding intercepts and graphing various linear equations.
2.1 relations and functions
This document defines key concepts related to functions and relations including:
- Relations are sets of ordered pairs with a domain and range
- A function is a special type of relation where each element in the domain is mapped to only one element in the range (no repeated x-values)
- Relations can be represented as ordered pairs, tables, graphs, or mappings
- The document provides examples of determining if a relation represents a function based on whether the domain elements are repeated
2.7 a graphing piecewise functions
Graphing piecewise functions involves graphing step-functions. Step-functions are functions defined by different formulas on different intervals of the domain that create a graph that looks like steps. The objective is to graph these types of piecewise functions by determining the formulas used on each interval and plotting the corresponding points to create the step-like graph.
Interval notation
Interval notation is used to represent sets of numbers graphically or through inequalities. The objectives are to become familiar with interval notation and to use it to represent sets of numbers given in graphical or inequality form in 3 sentences or fewer.
1.7 solving absolute value equations part 2
1. Absolute value equations can be solved by isolating the absolute value expression and setting up two separate equations, one with the expression unchanged and one with the expression negated.
2. The document provides examples of solving various absolute value equations including |x + 8| = 3, |y + 4| - 3 = 0, and 6|5x + 2| = 312.
3. Key steps are to isolate the absolute value expression, set up the two equations, solve each equation separately, and check the solutions.
1.7 solving absolute value equations part 1
Absolute value equations can be solved by isolating the absolute value expression, setting up two equations where one drops the absolute value bars and the other negates the expression inside, and solving each equation. For example, to solve 6|5x + 2| = 312, one would isolate the absolute value term to get |5x + 2| = 52, set up the equations 5x + 2 = 52 and 5x + 2 = -52, solve to get x = 10 and x = -10.8, and check that the solutions satisfy the original equation.
1.2 algebraic expressions and models
1. The document discusses evaluating and simplifying algebraic expressions by combining like terms. It covers evaluating powers, using order of operations, substituting values for variables, and combining like terms.
2. Examples are provided to demonstrate evaluating powers, using order of operations to solve expressions, substituting values into algebraic expressions, and simplifying expressions by combining like terms.
3. Applications are given involving modeling Hawaii's population growth and the mileage on a used car to reinforce the concepts.
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1.4 rewriting equations and formulas
- 1. Rewriting Equations & Formulas Today’s objectives (September 1, 2009): 1. I will rewrite equations with more than one variable. 2. I will rewrite common formulas.
- 2. Substitute the value of x into the equation and then solve for y. Original equation. xy + 3x = 6; x = 1 Substitution. (1)y + 3(1) = 6 Multiplication. y + 3 = 6 Subtract 3. y=3
- 3. Solve for y and then substitute the value of x into the equation. Original equation. 4x – 3xy = 5; x = 1 Solve for y. Subtract 4x. -3xy =5 – 4x Divide by -3x. y = (5 – 4x)/-3x Substitution. y = (5 – 4(1))/-3(1) Multiply. y = ( 5 -4)/-3 Simplify. y = -1/3
- 4. Solve the equation for the indicated variable. Solve for h. Original equation. A= (h/2)(b1 + b2) Multiply by 2. 2A = h(b1 + b2) Divide by (b1 + b2). 2A/(b1 + b2) = h(b1 + b2)/ (b1 + b2) Simplify. 2A/(b1 + b2) = h
- 5. Solve the equation for the indicated variable. Solve for b1. Original equation. A= (h/2)(b1 + b2) Multiply by 2. 2A = h(b1 + b2) Divide by h. 2A/h = h(b1 + b2)/h Simplify. 2A/h = b1 + b2 Subtract b2. 2A/h - b2 = b1