Solving Inequalities

1. Solving Inequalities

2. 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.

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

4. 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

5. 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.

6. 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.

7. -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

8. Try these: • Solve2x+3>x+5 • Solve- c - 11>23 • Solve3(r-2)<2r+4

9. Properties of Inequalities • Transitive Property If a b and b c, then a c • Addition Property If a b then a + c b + c • Subtraction Property If a b then a –c b - c

10. Properties of Inequalities • Multiplication Property If a < b, and c > 0, then ac < bc If a < b, and c < 0, then ac > bc • Division Property If a < b, and c > 0, then a/c < b/c If a < b, and c < 0, then a/c > b/c