1. 1.graph inequalities on a number line. 2.solve inequalities using addition and subtraction. Objective The student will be able to:

2. 6) Solve x + (-14) < 16 x - 14 < 16 + 14 + 14 x < 30 30 + (-14) = 16 16 = 16 Solve this problem like an equation 1.Draw “the river” 2.Eliminate double signs 3.Add 14 to both sides 4.Simplify 5.Check your answer 6.Graph the solution o 303129

3. 7) Solve y + 21 ≥ 7 - 21 -21 y ≥ -14 (-14) + 21 = 7 7 = 7 1.Draw the “river” 2.Subtract 21 from both sides 3.Simplify 4.Check your answer 5.Graph the solution -14-13-15 ●

4. 8) Solve 8y + 3 > 9y - 14 o 171816 - 8y - 8y 3 > y - 14 + 14 + 14 17 > y y < 17 8(17) + 3 = 9(17) - 14 1.Draw “the river” 2.Subtract 8y from both sides 3.Simplify 4.Add 14 to both sides 5.Simplify 6.Rewrite inequality with the variable first 7.Check your answer 8.Graph the solution

5. 10) Solve 3r - 17 ≥ 2r + 14 ● 313230 - 2r - 2r r – 17 ≥ 14 + 17 + 17 r ≥ 31 3(31) - 17 = 2(31) + 14 1.Draw “the river” 2.Subtract 2r from both sides 3.Simplify 4.Add 17 to both sides 5.Simplify 6.Check your answer 7.Graph the solution

6. 11) Solve -2x + 6 ≥ 3x - 4 1.x ≥ -2 2.x ≤ -2 3.x ≥ 2 4.x ≤ 2 Answer Now

7. 12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? Answer Now 1.96 2.97 3.98 4.100

8. Solve p – 4 < 1. Graph the solutions. p – 4 + 4 < 1 + 4Add 4 to each side. p < 5Simplify. 10-2

9. Solve 8 d – 2. Graph and check your solution. > 8 + 2 d – 2 + 2Add 2 to each side. > 10 d, or d 10Simplify. >< Check: 8 = d – 2Check the computation. 8 10 – 2Substitute 10 for d. 8 = 8 8 d – 2Check the direction of the inequality. 8 9 – 2Substitute 9 for d. 8 7 > > >

10. Additional Example 1A: Using Addition and Subtraction to Solve Inequalities Solve the inequality and graph the solutions. x + 12 < 20 –12 x + 0 < 8 x < 8 Since 12 is added to x, subtract 12 from both sides to undo the addition. –10 –8 –6–4 –2 0246810 The solution set is {x: x < 8}.

11. d – 5 > –7 Since 5 is subtracted from d, add 5 to both sides to undo the subtraction. The solution set is {d: d > –2}. +5 d + 0 > –2 d > –2 d – 5 > –7 Additional Example 1B: Using Addition and Subtraction to Solve Inequalities Solve the inequality and graph the solutions. –10 –8 –6–4 –2 0246810

12. a. s + 1 ≤ 10 Check It Out! Example 1 –1 s + 0 ≤ 9 s ≤ 9 Since 1 is added to s, subtract 1 from both sides to undo the addition. Solve each inequality and graph the solutions. s + 1 ≤ 10 9 –10 –8 –6–4 –2 0246810 The solution set is {s: s ≤ 9}.

13. 2x + 3 > x + 5

14. a - 12 < 6 2x ≤ x + 1

15. 3x – 9 ≤ 2x + 6