Solving Inequalities Lesson 7.6

Solving Inequalities An inequality is a math sentence with an inequality symbol instead of an “=“ sign. Ex. > < > < To solve an inequality means to find the set of numbers that could replace the variable. To graph an inequality means to show the set of points on a number line that represents the solution.

Solving Inequalities Example 1 – Graph the following. All numbers greater than -2 x > -2

Your Turn Question #1 – Graph the following. All numbers less than 3 A) B) C) D) x < 3

Solving Inequalities Example 2 – Graph the following. All numbers less than or equal to 4 x < 4

Your Turn Question #2 – Graph the following. All numbers greater than or equal to -2 A) B) C) D) x > -2

Your Turn Question #3 – Write an inequality that represents the following graph. A) x > -3 B) x > -3 C) x < -3 D) x < -3 -3 x < -3

Your Turn Question #4 – Write an inequality that represents the following graph. 3 A) x > 3 B) x > 3 C) x < 3 D) x < 3 x > 3

Solving Inequalities To solve an inequality is exactly like solving equations. Example 3 – Solve the following inequality. 72 < g – 13 72 < g – 13 +13 +13 85 < g g > 85 80

Solving Inequalities Question #5 – Solve the following inequality. A) -59 > t B) -31 > t C) 59 > t D) 31 > t 45 > t + 14 -14 -14 31 > t t < 31 30 31

Solving Inequalities When dividing or multiplying by a negative number, reverse the direction of the inequality symbol. Example 4 – Solve the following inequality. -7b < 42 -7b < 42 -7 -7 b > -6 -6

Your Turn Question #6 – Solve the following inequality. -64 > -4p A) 16 > p B) -16 > p C) 16 < p D) -16 < p -64 > -4p -4 -4 16 < p p > 16 16 20

Your Turn Question #7 – Solve the following inequality. -5c – 7 > 8 +7 +7 A) c > -3 B) c > -75 C) c < -3 D) c < -75 -5c > 15 -5 -5 c < -3 -3

Homework Assignment Page 348 #17, 18, 21, 26-32

Sunshine State Standards (http://www. floridastandards MA.D.2.3.1 – graph solutions of inequalities on a number line.