1. ABSOLUTE VALUE INEQUALITIES

2.  Just like absolute value equations, inequalities will have two solutions: |3x - 2| ≤ 7 3x – 2 ≤ 7 +2 +2 3x ≤ 9 x ≤ 3 -5/3 ≤ x ≤ 3 [ -5/3, 3 ] -7 ≤ 3x – 2 +2 -5 ≤ 3x -5/3 ≤ x -7≤ 3x – 2 ≤ 7

3. ABSOLUTE VALUE INEQUALITIES  Try again:  |2x + 1| < 11  -11 < 2x +1 AND  -12 < 2x  -6 < x  2x +1 < 11  2x < 10  x < 5 -6 < x < 5 ( -6, 5 )

4. ABSOLUTE VALUE INEQUALITIES  If the sign is less than, the answer is written as one statement. |2x + 1| < 11 -6 < x < 5 (-6, 5)  If the sign is greater than, the answer must be written as two statements. See the next problem.

5. ABSOLUTE VALUE INEQUALITIES  |1 – 2x| > 5  1 – 2x > 5 -1 -1 -2x > 4 x < -2 OR  1 – 2x < -5 -1 -1 -2x < -6 x > 3 x 3 (-∞, -2) U ( 3, ∞)

6. ABSOLUTE VALUE INEQUALITIES  Practice these:  |2x - 5| < 6  |3x + 6| ≤ 3  |x - 5| > 4  |2x + 5|≥ 8