WU 36 Solve: 1. |x – 4| = 9 |7x – 2| = 5 |3x – 2| + 4 = 21

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Presentation transcript:

WU 36 Solve: 1. |x – 4| = 9 |7x – 2| = 5 |3x – 2| + 4 = 21 Write the inequality shown: 4. 5. -3 2 -4 4

9.4 Inequalities and Absolute Value

2 Cases |A| >b Disjunction A<-b or A>b |A| <b Conjunction Case 1: Less Than Case 2: Greater Than |A| <b Conjunction -b<A<b |A| >b Disjunction A<-b or A>b

Solve and graph: |x + 2|  5 x + 2 = -5 x + 2 = 5 x = 3 x = -7  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 To solve an inequality of the form |A| < b, where b is a positive number, we solve the conjunction –b < A < b.

Solve and graph: |4x - 10| > 2  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 Solve for both end points. Write solution as disjunction (x< 2 or x > 6)

Solve and graph: |3x - 8|  5 3x - 8 = 5 3x = 13  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 To solve an inequality of the form |A| > b, where b is a positive number, we solve the disjunction A < -b or A > b.

Solve and graph: |3x|  18 x = 6 x = -6 -6  x  6  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 To solve an inequality of the form |A| < b, where b is a positive number, we solve the conjunction –b < A < b.

Solve and graph: |3x – 4 |  2 x = 2 2/3  x  2  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8

Solve and graph: |4x – 9 |  7 x = 4  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8

Solve and graph: |3x +4 |  19 x = 5  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8

Solve and graph: |7x + 4 |+ 6  2  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8

Solve :

Assignment: Page 415 (2-38) even