1. Entry Task Solve for the given variable 1) A = ½bh for h 2) ax + bx = c solve for x LT: I can solve and graph inequalities.

2. 1.6 Solving Inequalities Target: I can solve and graph inequalities. Write and solve compound inequalities. LT: I can solve and graph inequalities.

3. Solving Inequalities ● Solving inequalities follows the same procedures as solving equations. ● There are a few special things to consider with inequalities: ● We need to look carefully at the inequality sign. ● We also need to graph the solution set. LT: I can solve and graph inequalities.

4. Review of Inequality Signs > greater than < less than greater than or equal less than or equal LT: I can solve and graph inequalities.

5. How to graph the solutions > Graph any number greater than... open circle, line to the right < Graph any number less than... open circle, line to the left Graph any number greater than or equal to... closed circle, line to the right Graph any number less than or equal to... closed circle, line to the left LT: I can solve and graph inequalities.

6. Solve the inequality: x + 4 < 7 -4 -4 x < 3 Subtract 4 from each side. Keep the same inequality sign. Graph the solution. Open circle, line to the left. 30 LT: I can solve and graph inequalities.

7. There is one special case. Sometimes you may have to reverse the direction of the inequality sign!! That only happens when you multiply or divide both sides of the inequality by a negative number. LT: I can solve and graph inequalities.

8. Example: Solve: -3y + 5 >23 -5 -5 -3y > 18 -3 -3 y < -6 Subtract 5 from each side. Divide each side by negative 3. Reverse the inequality sign. Graph the solution. Open circle, line to the left. 0-6 LT: I can solve and graph inequalities.

9. 2x < -6 and 3x ≥ 12 1. Solve each inequality for x 2. Graph each inequality 3. Combine the graphs 4. Where do they intersect? 5. They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -3 0-6 o -3 0-6 o 4 71 o ● 4 71 o ● LT: I can solve and graph inequalities.

10. Graph 3 < 2m – 1 < 9 Remember, when written like this, it is an AND problem! 3 < 2m – 1 AND 2m – 1 < 9 Solve each inequality. Graph the intersection of 2 < m and m < 5. 05 -5 LT: I can solve and graph inequalities.

11. Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-2) = 18 1.Subtract 12 from both sides 2.Simplify 3.Divide both sides by -3 4.Simplify (Switch the inequality!) 5.Check your answer 6.Graph the solution o -2 -3 LT: I can solve and graph inequalities.

12. Solve 26p - 20 > 14p + 64 -14p 12p – 20 > 64 + 20 + 20 12p > 84 12 12 p > 7 26(7) – 20 = 14(7) + 64 1.Subtract 14p from both sides 2.Simplify 3.Add 20 to both sides 4.Simplify 5.Divide both sides by 12 6.Simplify 7.Check your answer 8.Graph the solution o 7 8 6 LT: I can solve and graph inequalities.

13. Try these: Solve 2x+3>x+5 Solve - c - 11>23 Solve 3(r-2)<2r+4 LT: I can solve and graph inequalities.

14. Assignment P. 38 #10,22,25,34,38,40,44,48,50,51,52,56,59,55,68 Challenge – 62-65 LT: I can solve and graph inequalities.