6th Grade Math Textbook, Fundamentals

&KDSWHU 

Lesson 3-6 for exercise sets.

&KHFN<RXU3URJUHVVIII

Solve and graph each inequality. Check your work to justify your answer.

1. 7 n 21 2. 9 

3 x 3. 12 w 96

4.Discuss and Write Is x4 the solution to the inequality 3x12?

Justify your answer.

After you solve an inequality, you can use a number line to graph

and check the solution set.

Solve: 8 x 24 Graph:

 Divide both sides by 8 to isolate x.

 Simplify.

x 3

The solution set is the numbers less than 3.

Check:According to the solution set, 0 is a solution and 3 is not.

8 • 3 24 Substitute 3 for x. 8 • 0 24 Substitute 0 for x.

24  24 False 0  24 Tr u e

So the circle on the number line is correct. So the direction of the ray is correct.

? ?

24

8

3

1

8

8

1

1

x

24

8

8 x

8

Acceleration: Two-Step Inequalities

Solving a two-step inequality is similar to solving a two-step equation.

• First, apply the Addition or Subtraction Property of Inequality to isolate
  the term that contains the variable.


• Then apply the Multiplication or Division Property of Inequality to get
  the variable alone on one side.

Solve: 4 k 6  14

4 k 6  6  14  6 Add 6 to both sides.

4 k 20 Simplify.



k 5

The solution set is all numbers greater than 5.

Divide both sides by 4

and simplify.

20

4

5

1

4

4

1

1

k

Check:According to the solution set,

6 is a solution and 5 is not.

(4 • 6) 6 14 Substitute 6 for k.

24 6 14 Simplify.

18  14 Tr u e

(4 • 5) 6 14 Substitute 5 for k.

20 6 14 Simplify.

14  14 False

?



?



?



?



01234567 910 8

Think

All integers, fractions, and decimals

less than 3 are solutions.