4.4 Absolute Value 11/14/12

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

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 = 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

Solving Absolute Value problems: In General:

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. –

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 =

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

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 – – – = ? – 14 = ? 10 – – = ? – = ? 14 = = Rewrite as two linear equations. Then solve each equation. 9 – 3x3x =24

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

Homework 4.4 p.195 #26-36 even only