1. Objectives: 1.Graph (and write) inequalities on a number line. 2.Solve and graph one-variable inequalities. (Linear) 3.Solve and graph compound inequalities. (Linear) 4.Solve and graph ABSOLUTE VALUE inequalities. Warm Up: Solve the following Inequalities 1.-3(2x - 7) > 9 2.51 > -3(2x - 7)

2. I. Solving Compound Inequalities “AND” Example 1 : -2 < x + 2 ≤ 4 x + 2 ≤ 4 - 2 -2 x ≤ 2 -2 < x + 2 -2 - 2 -4 < x -4 < x ≤ 2 -4 -2 24 -2 < x + 2 ≤ 4 -2 - 2 -2 -4 < x ≤ 2 Test Value:-2 < -5 + 2 ≤ 4 -2 < -3 ≤ 4 Test Value:-2 < 0 + 2 ≤ 4 -2 < 2 ≤ 4 FALSETRUEFALSE Test Value:-2 < 4 + 2 ≤ 4 -2 < 6 ≤ 4

3. Example 2: -3 ≤ 2x + 1 ≤ 5 -1 - 1 -1 -4 ≤ 2x ≤ 4 2 2 2 -2 ≤ x ≤ 2 -2 2 I. Solving Compound Inequalities “AND” Test Value:-3 ≤ 2(-3) + 1 ≤ 5 -3 ≤ -5 ≤ 5 Test Value:-3 ≤ 2(0) + 1 ≤ 5 -3 ≤ 1 ≤ 5 Test Value:-3 ≤ 2(3) + 1 ≤ 5 -3 ≤ 7 ≤ 5 FALSETRUEFALSE

4. Example 3: -9 ≤ -3(2x + 7) ≤ 15 -9 ≤ -6x - 21 ≤ 15 +21 + 21 +21 12 ≤ -6x ≤ 36 -6 -6 -6 -2 ≥ x ≥ -6 -6-2 2 6 I. Solving Compound Inequalities “AND” Test Value:-9 ≤ -3(2(-7) + 7) ≤ 15 -9 ≤ 21 ≤ 15 Test Value: -9 ≤ -3(2(-5) + 7) ≤ 15 -9 ≤ 9 ≤ 15 -9 ≤ -3(2(0) + 7) ≤ 15 -9 ≤ -21 ≤ 15 FALSE TRUE

5. Example 5: 3x + 13 7 3x + 13 < 4 - 13 -13 3x < -9 3 x < -3 2x - 5 > 7 + 5 +5 2x > 12 2 x > 6 x 6 -6 -3 36 II. Solving Compound Inequalities “OR” Test Value:3(-5) + 13 7 -2 7 Test Value: TRUE FALSE 3(0) + 13 7 13 7 3(7) + 13 7 34 7

6. Example 6: 2(2x + 3) ≤ 2 or -7(3x – 5) < -7 2(2x + 3) ≤ 2 4x + 6 ≤ 2 - 6 -6 4x ≤ -4 4 x ≤ -1 -7(3x - 5) < -7 -21x + 35 < -7 - 35 -35 -21x < -42 -21 x > 2 x ≤ -1 or x > 2 -2 12 II. Solving Compound Inequalities “OR” TRUE FALSE Test Value:2(2(-2) + 3) ≤ 2 or -7(3(-2) – 5) < -7 -2 ≤ 2 or 77 < -7 Test Value: 2(2(0) + 3) ≤ 2 or -7(3(0) – 5) < -7 6 ≤ 2 or 35 < -7 2(2(3) + 3) ≤ 2 or -7(3(3) – 5) < -7 18 ≤ 2 or -28 < -7