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.

2. I. Solving Inequalities Using Addition and Subtraction 1. x + 15 > -13 - 15 -15 x > -28 -2828 Test Value:-29 + 15 > -13 -14 > -13 FALSE Test Value:0 + 15 > -13 15 > -13 True

3. I. Solving Inequalities Using Addition and Subtraction 2. x - 8 ≥ -21 + 8 +8 x ≥ -13 -1313 Test Value:-14 - 8 ≥ -21 -22 ≥ -21 Test Value:0 - 8 ≥ -21 -8 ≥ -21 False True

4. I. Solving Inequalities Using Addition and Subtraction 3. 5 x > 35 5 5 x > 7 -77 Test Value:5(0) > 35 0 > 35 Test Value:5(8) > 35 40 > 35 FalseTrue

5. 4. -3 x > -48 -3 -3 x < 16 -1616 I. Solving Inequalities Using Addition and Subtraction RULE: WHENEVER YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER, YOU MUST FLIP THE INEQUALITY SIGN Test Value:-3(0) > -48 0 > -48 Test Value:-3(20) > -48 -60 > -48 TrueFalse

6. 5. -5x - 75 > -40 + 75 +75 -5x > 35 -5 -5 x < -7 I. Solving Inequalities Using Addition and Subtraction 6. -4x - 437 > 8x + 19 +4x -437 > 12x +19 -19 -456 > 12x 12 -38 > x

7. 7. -5(5x + 3) > -85 -25x - 15 > -85 + 15 +15 -25x > -70 -25 x < 14/5 I. Solving Inequalities Using Addition and Subtraction 8. 2x + 3 < 2x - 8 -2x 3 < -8 Since we are left with a FALSE statement that means this inequality has NO SOLUTION 9. 2x - 5 < 2x - 1 -2x -5 < -1 Since we are left with a TRUE statement that means this inequality has INFINITELY MANY SOLUTIONS