Unit 8 6 part 1
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This document provides instructions on how to solve rational equations. It explains that you first find the least common denominator, then multiply both sides by the LCD to eliminate fractions. You then simplify the equation and solve for the variable. To check your work, plug your solution back in and see if both sides are equal. The document includes two example problems to practice these steps, showing the work and solutions.
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This document discusses various topics in solving linear equations in one variable including:
1) The difference between identity equations that are true for all values and conditional equations that are only true for some values.
2) How to solve linear equations by producing equivalent equations through distributing, combining like terms, and clearing fractions.
3) How to find the x-intercept and y-intercept of a linear equation algebraically by setting one variable equal to zero and solving for the other.
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Rational equations are equations where a variable occurs in the denominator of a rational expression. To solve rational equations:
1) Identify values that result in no solution by finding values where the denominator equals 0.
2) Find the lowest common denominator (LCD) and multiply both sides of the equation by the LCD.
3) Solve the numerators and reject any solutions that result in the denominator equaling 0.
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1) Solving a simple rational equation with a single rational expression on each side. The solutions are -6 and 2.
2) Solving a rational equation with rational expressions on both sides. The solution appears to be 2, but it is an extraneous solution.
3) Solving a rational equation by factoring the denominators to find the least common denominator (LCD).
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This document provides an overview of a lesson on solving and graphing inequalities. It includes student objectives like understanding properties of inequalities and learning how to solve singular and absolute value inequalities. Examples are provided to demonstrate solving different types of inequalities step-by-step and graphing the solutions. Real-world examples like parking restrictions are used to illustrate how inequalities apply in daily life. Formative assessments like a KWL chart and discussion questions are incorporated to check understanding.
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1) The difference between identity equations that are true for all values and conditional equations that are only true for some values.
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3) How to find the x-intercept and y-intercept of a linear equation algebraically by setting one variable equal to zero and solving for the other.
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Rational equations are equations where a variable occurs in the denominator of a rational expression. To solve rational equations:
1) Identify values that result in no solution by finding values where the denominator equals 0.
2) Find the lowest common denominator (LCD) and multiply both sides of the equation by the LCD.
3) Solve the numerators and reject any solutions that result in the denominator equaling 0.
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This document discusses solving rational equations by using the cross product property. It provides three examples of solving rational equations:
1) Solving a simple rational equation with a single rational expression on each side. The solutions are -6 and 2.
2) Solving a rational equation with rational expressions on both sides. The solution appears to be 2, but it is an extraneous solution.
3) Solving a rational equation by factoring the denominators to find the least common denominator (LCD).
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The document provides instructions and examples for solving rational equations and inequalities. It explains that multiplying both sides of a rational equation by the least common denominator eliminates fractions. Students are advised to check their solutions and watch out for extraneous solutions. The steps for solving rational inequalities are given as identifying domain restrictions, moving everything to one side, solving, and drawing vertical lines to indicate intervals on the number line. Two sample SAT questions related to rational expressions are also included.
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This document discusses solving rational equations and inequalities. It begins with definitions of rational equations and inequalities. Examples are provided to demonstrate how to solve rational equations by multiplying both sides by the least common denominator to eliminate fractions. The document notes that extraneous solutions may arise and must be checked. Methods for solving rational inequalities using graphs, tables, and algebra are presented. Practice problems are included for students to test their understanding.
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This document provides instructions on how to solve rational equations. It explains that you first find the least common denominator, then multiply both sides by the LCD to eliminate fractions. You then simplify the equation and solve for the variable. To check your work, plug your solution back in and see if both sides are equal. The document includes examples of solving two practice rational equations for the variables N and W.
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Here are the steps to solve each absolute value inequality:
1) 4m - 5 > 7 or 4m - 5 < -9
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This document provides instructions on how to solve rational equations. It explains that you first find the least common denominator, then multiply both sides by the LCD to eliminate fractions. You then simplify the equation and solve for the variable. To check your work, plug your solution back in and see if both sides are equal. The document includes examples of solving two practice rational equations for the variables N and W.
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This document appears to be notes from a math class covering systems of inequalities and equations. It includes examples of solving systems of equations by elimination and substitution. It provides step-by-step instructions for setting up and solving systems using both methods. It also shows examples of applying systems of equations to word problems involving tickets sales and math test points.
LEARNING PLAN IN MATH 9 Q1W1
This document outlines a learning plan for a 9th grade mathematics class on patterns and algebra for the first quarter. It includes standards, competencies, lessons, activities and a performance task on solving quadratic equations using different algebraic methods. Students will compare the methods and apply them to design classroom fixtures using measurements and equations. The plan provides instruction, practice and assessments to help students master solving quadratic equations and transfer their knowledge to real-world problems.
Solving 2 step equations
This document provides instructions for solving two-step equations. It explains that two-step equations require breaking the problem into two steps - the first step involves adding or subtracting, while the second step involves multiplying or dividing. Several examples are worked through step-by-step to demonstrate the process of isolating the variable by first undoing addition/subtraction and then undoing multiplication/division. Students are provided practice problems and instructed to show their work.
Lab1
This lab document introduces the dfield7 tool in Matlab for investigating and visualizing solutions to first order differential equations. Students are instructed on how to use dfield7 to plot direction fields and solution curves for different equations. They are then given 5 problems to solve using dfield7, estimating solutions to initial value problems for various differential equations by placing points on the graphs or entering values numerically. The document concludes by noting dfield7 can quickly solve first order DEs and hints that future labs will cover higher order and systems of DEs.
Lab1
This lab document introduces the dfield7 tool in Matlab for investigating and visualizing solutions to first order differential equations. Students are instructed on how to use dfield7 to plot direction fields and solution curves for different equations. They are then given 5 problems to solve using dfield7, estimating solutions to initial value problems for various differential equations by placing points on the graphs or using keyboard input. The document concludes by noting dfield7 can quickly solve first order DEs and hints that future labs will cover higher order and systems of DEs.
taller de fisica
This lab document introduces the dfield7 tool in Matlab for investigating and visualizing solutions to first order differential equations. Students are instructed on how to access dfield7 within Matlab and are given examples of its basic functions like plotting solution curves from initial conditions. The document then lists 5 practice problems for students to solve using dfield7, obtaining approximate solutions to initial value problems for different first order differential equations by placing the cursor or entering values at specific points on the direction field graphs.
Lesson 10
This document provides the lesson plan and materials for a math lesson on using arrays to model multiplication. The lesson includes:
- Fluency practice multiplying by 2s
- An application problem about multiplying the number of guitar strings on multiple guitars
- Using arrays to represent the total number of guitar strings as rows and columns, and writing multiplication sentences to describe the arrays
- Discussing how the distributive property allows breaking the array into parts that are multiplied and added
- Having students practice using this method to model other multiplication problems
Similar to Unit 8 6 part 1 (20)
Unit 8 6 part 1
- 1. Intro Video
- 2. UNIT 8-6 Solving Rational Equations and Simplifying Expressions
- 3. Section 1!!! Here, you will learn how to solve rational equations!!!
- 4. How To Solve To start, you first need to find the Least Common Denominator (or LCD)! LCD= (28)(Z+2)
- 5. How To Solve You then multiply by the LCD, to get rid of the denominator.
- 6. How To Solve Now, you just simplify the equation and solve for X.
- 7. How To Check First, you plug in the amount you got for the variable, and simplify.
- 8. How To Check Then, you combine like terms, and make the 2 fractions on the right side have a common denominator, so they can be combined.
- 9. How To Check Finally, you combine like terms again… and simplify. If both sides are equal to each other, then your answer is correct, if not, you may want to go back and check your work.
- 11. Practice #1 In the equation (1/n+2)+(1/n-2)=(3/n2-4), what is N?
- 12. Practice #1 In the equation (1/n+2)+(1/n-2)=(3/n2-4), what is N?
- 13. Practice #1 In the equation (1/n+2)+(1/n-2)=(3/n2-4), what is N?
- 14. Did You know It? The correct answer was… N=3/2! Your work should have looked something like this.
- 15. Practice #2 In the equation… What is W?
- 16. Practice #2 In the equation… What is W?
- 17. Practice #2 In the equation… What is W?
- 18. Did You Know It? The correct answer was…W=-2! Your work should have looked like this.