1. Lesson 8.1

2. » A statement where two mathematical expressions are. » Think of an equation as a balance scale or teeter-totter. The left side must always be balanced by the right. » In an algebraic equation, the value of the variable that makes the equation true is the of the equation. EQUAL SOLUTION The equation 3x = 12 has only one solution, x =. The equation does not hold true for any other value of x. 4

3. » To solve an equation we must get the variable ! » To do this we use inverse operations. Inverse means ! opposite ALONE

4. Solving algebraic equations involving… x + 6 – 6 < 9 x + 6 – 6 = 9 - 6

5. x + 6 = 9 – 6 – 6 x = 3 x = gives the solution of the equation x + 6 = 9 Check: Substitute for the value of x into the equation. x + 6 = When x =, the equation x + 6 = 9 is true. Subtract 6 from both sides 3 3 3 + 6 = 9 3

6. 6 = x – 3 +3 + 3 9 = x Add 3 to both sides of the equation Check: Substitute for the value of x into the equation. 6 = x - 3 When x =, the equation 6 = x - 3 is true. Solving algebraic equations involving… 9 = 9 – 3 = 6 9

7. Solving algebraic equations involving…

8. 2x = 12 x = 6 x = gives the solution of the equation 2x = 12 Check: Substitute for the value of x into the equation. 2x = When x =, the equation 2x = 12 is true. Divide both sides by 2. 2 6 6 = 12 6

9. Solving algebraic equations involving… Multiply both sides by 3 12 = 4 12

10. Solving algebraic equations involving… Simplify.

11. Solving algebraic equations involving… Divide both sides by 3. Flip and multiply!

12. Solving algebraic equations involving… Flip and multiply! 1 9 y = 27

13. x + 8 = 19 - 8 - 8 x = 11 w – 6 = 10 + 6 + 6 w = 16 3x = 27 x = 9 3 3

15. » Goal: To get the variable alone! » With multiple operations we have to undo the order of operations! 3x - 4 = 11 + 4 + 4 3x = 15 x = 5 3 3 Add 4 to both sides. Divide both sides by 3.

16. 3x - 4 = 17 + 4 + 4 3x = 21 x = 7 4p + 9 = 45 - 9 - 9 4p = 36 p = 9 3 3 4 4