1. Solving Inequalities
Lesson 7.6

2. 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.

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

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

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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

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

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