1. Solve Linear Equations Chapter 1.3

2. Equations and Expressions

3. Equations Are Statements

4. Solving Equations

5. Solving Equations

6. Properties of Equality

7. Properties of Equality

8. Solving a Linear Equation

9. Solving a Linear Equation

10. Solving a Linear Equation In the process of solving an equation, we change the original equation to a different one But because of the properties of equality, we are assured that the new equations have the same solution as the original These new equations are called equivalent equations because they have the same solution Now let’s see how we can use the number properties to solve an equation As we have done up to now, we will justify our steps

11. Solving a Linear Equation Given 1.Property of equality 2.Assoc. Prop. Add. 3.Inv. Prop. Add. 4.Ident. Prop. Add. 5.Property of equality 6.Assoc. Prop. Mult. 7.Inv. Prop. Mult. 8.Ident. Prop. Add. 9.Ident. Prop. Add. & Mult.

12. Solving a Linear Equation As before, you need not show every step; you may use the method you learned in past years However, it will to your benefit later if, rather than thinking of “dividing both sides”, you think of “multiply both sides by the reciprocal” The following example will illustrate why this is better

13. Solving a Linear Equation Given 1.Property of equality 2.Assoc. Prop. Add. 3.Inv. Prop. Add. 4.Ident. Prop. Add. 5.Property of equality 6.Assoc. Prop. Mult. 7.Inv. Prop. Mult. 8.Ident. Prop. Add. 9.Ident. Prop. Add. & Mult.

14. Variations In the next few examples I will use the same step-by-step method, but you need not do this on your howework However, you may be asked to name steps on a quiz or test! We will next look at variations of linear equations: with variables on both sides of the equation; with variables in parentheses But first, work the following example problems in your notes

15. Guided Practice

19. Variables on Both Sides of the Equal Sign

21. Variables in Parentheses Some equations may have variables within parentheses If the parentheses are multiplied by something, then we must use the distributive property to remove the parentheses If nothing multiplies the parentheses, they are unneeded and may be dropped Once parentheses are removed, it may be necessary to combine like terms on one or both sides of the equal sign Remember! You cannot combine like terms that are on opposite sides of the parentheses

22. Variables in Parentheses

23. Guided Practice

24. Exercise 1.3 Page 21, #3-18 Page 21, #21-31, odds Page 22, #33-39, odds Page 22, #55-61, odds Total: 30 problems