Solving Inequalities

1. 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.

2. Review of Inequality Signs > greater than < less than greater than or equal less than or equal

3. 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

4. 0 3 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.

5. Can we always undo and keep the inequality true? • Let’s investigate: • 2 < 6 • Adding to both sides? • 2 + 2 < 6 + 2 • Subtracting on both sides? • 2 – 2 < 6 - 2

6. Can we always undo and keep the inequality true? • Let’s investigate: • 2 < 6 • Multiply both sides? • 2 ∙ 2 < 6 ∙ 2 • Dividing on both sides? • 2 2 < 6 2

7. So far so good? • What about multiplying and dividing by a negative number?: • 2 < 6 • Multiply both sides by -2? • 2 ∙ -2 < 6 ∙ -2 • If we multiply or divide by a negative number we need to flip the inequality sign.

8. There is one special case. • You only reverse the inequality sign when when you multiply or divide both sides of the inequality by a negative number.

9. -6 0 Example: • Subtract 5 from each side. • Divide each side by negative 3. • Reverse the inequality sign. • Graph the solution. • Open circle, line to the left. Solve:-3y + 5 >23 -5-5 -3y > 18 -3 -3 y < -6

10. Try these: • Solve2x+3>x+5 • Solve- c - 11>23 • Solve

11. Homework: • Pg 572 #2 to 12 even • Pg. 572 #22 to 30 even • Pg. 573 #2 to 16 even