The document provides an overview of lessons on linear equations for a math class over 3 days. Key points covered include: - Day 1 focuses on defining linear equations, properties of equality, and solving linear and rational equations. - Day 2 covers solving equations involving radicals, absolute values, and literal equations. - Day 3 involves word problems including number, geometry, digit, investment, age, mixture, uniform motion, work, and clock problems, which are modeled and solved using linear equations.

1. MATH10 ALGEBRA LINEAR EQUATIONS Week 1 Day 1 Linear Equations (Algebra and Trigonometry, Young 2 nd Edition, page 90-99)

4. An equation is a statement that two mathematical expressions are equivalent or equal. DEFINITION EQUATION The values of the unknown that makes the equation true are called solutions or roots of the equation, and the process of finding the solution is called solving the equation. Example: Week 1 Day 1

9. EXAMPLE Determine whether the given equation is an identity or a conditional equation. Week 1 Day 1

13. DEFINITION LINEAR EQUATION IN ONE VARIABLE A linear equation in one variable is an equation that can be written in the form a x + b = 0 where a and b are real numbers and a  0 Example: 2 x – 1 = 0, -5 x = 10 + x , 3 x + 8 = 2 Week 1 Day 2

14. Nonlinear; contains the square of the variable Nonlinear; contains the reciprocal of the variable Nonlinear; contains the square root of the variable Week 1 Day 2 Linear Equations Nonlinear Equations

15. SOLVING A LINEAR EQUATION IN ONE VARIABLE Steps 1. Simplify the algebraic expressions on both sides of the equation. 2. Gather all the variable terms on one side of the equation and all constant terms on the other side. 3. Isolate the variable. 4. Check the solution by substituting the value of the unknown into the original equation. Week 1 Day 2

16. EXAMPLE Problem #23 on page 97 Week 1 Day 2 Solve for the indicated variable: 2(x-1)+3=x-3(x+1) STEP DESCRIPTION EXAMPLE 1 Simplify the algebraic expression on both sides 2(x-1)+3 = x-3(x+1) 2x-2+3 = x-3x-3 2x+1 = -2x-3 2 Gather all the variables on one side of the equation and all constant terms on the other side. 2x+2x = -3-1 4x = -4 3 Isolate the variable

17. Solve the following equations. Week 1 Day 2

18. Linear Equations Involving Fractions. Week 1 Day 2

19. SOLVING RATIONAL EQUATIONS THAT ARE REDUCIBLE TO LINEAR EQUATIONS A rational equation is an equation that contains one or more rational expressions. Extraneous solution are solutions that satisfy a transformed equation but do not satisfy the original equation. Steps 1. Determine any excluded values(denominator equals 0). 2. Multiply the equation by the LCD. 3. Solve the resulting linear equation. 4. Eliminate any extraneous solution. Week 1 Day 2

20. Solve the following equations. EXAMPLE Week 1 Day 2

23. SOLVING EQUATIONS USING RADICALS Week 1 Day 3

24. Solve each equations: Week 1 Day 3

25. ABSOLUTE VALUE EQUATIONS DEFINITION The absolute value of a number a is given by Week 1 Day 3

26. Solve each equations: (examples on page 131) Solve each equations: EXAMPLE Week 1 Day 3

27. SOLVING FOR ONE VARIABLE IN TERMS OF THE OTHER Many formulas in the sciences involve several variables, and it is often necessary to express one of the variables in terms of the others. Week 1 Day 3

29. CLASSWORK HOMEWORK #s 31,33,35,43,46,51,55,57,61, 65 page 97-98 #s 32, 34, 42, 60 page 97 Week 1 Day 3

30. APPLICATION INVOLVING LINEAR EQUATIONS Week 2 Day 1 Application Involving Linear Equations (Algebra and Trigonometry, Young 2 nd Edition, page 100-113).

33. Start Read and analyze the problem Make a diagram or sketch if possible Determine the unknown quantity. Did you set up the equation? Set up an equation, assign variables to represent what you are asked to find. A no yes A Solve the equation Check the solution Is the unknown solved? no yes End Week 2 Day 1

50. CLASSWORK HOMEWORK #s 15,19,31,34,38,42,44,47,50,73 page 110-113 Classroom example 1.2.6 page 106 and 1.2.7 page 108 Week 2 Day 3