1. 4.4 Absolute Value 11/14/12

2. Absolute Value: The distance of a number from 0 on a number line. Written as l x l Ex. |5| (distance of 5 from 0) = 5 Ex. |-8| (distance of -8 from 0) = 8 Distance is never negative. which means |x| = -x

3. What value of x would make what’s inside | | 7 or -7 Ex 1: Solve for x |7| or |-7| x + 2 = 7 and x + 2 = -7 - 2 -2 - 2 -2 x = 5 x = -9 Check: x = 5 |5 + 2| = 7 |7| = 7 7 = 7 x = -9 |-9 + 2| = 7 |-7| = 7 7 = 7 What value of x would make what’s in | | 7 or -7? |x + 2| = 7

4. Solving Absolute Value problems: In General:

5. Solve an Absolute Value Equation Example 2 Solve 2x2x – 5 = 9.9. SOLUTION Rewrite the absolute value equation as two linear equations.Then solve each equation. 2x2x – 5 =9 Write original equation. 2x2x – 5 =9 or 2x2x – 5 =9 – Expression can equal 9 or 9. – or – 2x2x = 4 – 2x2x = 14 – Subtract 5 from each side. – x = 2orx = 7 Divide each side by 2. –

6. Solve an Absolute Value Equation Example 2 ANSWER The equation has two solutions: 2 and 7. Check the solutions. – CHECK () 2 – 2 – 5 9 = ? () 7 2 – 5 9 = ? () 4 – – 5 9 = ? 14 – 5 9 = ? 9 9 = ? = ? 9 9 – 9 9 = ? 9 9 =

7. Solve an Absolute Value Equation Example 3 Solve 109 – 3x3x = 14. – SOLUTION First isolate the absolute value expression on one side of the equation. Write original equation. 109 – 3x3x =14 – Add 10 to each side. =24 9 – 3x3x

8. Solve an Absolute Value Equation Example 3 =24 9 – 3x3x or =24 9 – 3x3x – =33 3x3x or=15 3x3x – Add 9 to each side. =11 x or =5 x – Divide each side by 3. The equation has two solutions: 11 and -5. Check the solutions. CHECK 9 () 11 – 3 14 = ? 10 – 9 () 5 – 3 14 = ? 10 – – 24 10 – = ? 14 24 – 14 = ? 10 – 24 10 – = ? 14 24 10 – = ? 14 = = Rewrite as two linear equations. Then solve each equation. 9 – 3x3x =24

9. Checkpoint Solve an Absolute Value Equation Solve the absolute value equation and check your solutions. 1. 2 x += 5 2. 6 x – = 7 ANSWER 3, 7 – ANSWER 13, 1 – 3. 7 2x2x – = 15 ANSWER 11, 4 – 4. 2x2x 1 – = 9 ANSWER 4, 5 – 5. 6 3x3x + 4 + 4 = ANSWER 2 – 1 – 6. 3 4x4x – = 2 ANSWER 1.5, 0

10. Homework 4.4 p.195 #26-36 even only