The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 3.12: SOLVING INEQUALITIES WITH VARIABLES

ON ONE SIDE

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To solve an inequality with a variable on one side, follow the steps below:

1. Add the same number to or subtract the same number from both sides to isolate the
   variable.


2. Multiply or divide both sides of the inequality by the same nonzero number so that the
   coefficient of the variable is 1.


3. When you multiply or divide both sides of the inequality by the same negative number,
   switch the direction of the inequality symbol.

EXAMPLES

Solve each inequality.

3 x+ 4 > 10 − 2 x− 8 > 10 2 + 5 x≤− 13

− 4 − 4 + 8 + 8 − 2 − 2

3 x> 6 − 2 x> 18 5 x≤− 15

3 x

3

>

6

3

− 2 x

− 2

<

18

− 2

5 x

5

≤

− 15

5

x> 2 x<− 9 x≤− 3

DIRECTIONS: Solve each inequality.

1. x− 4 > 3 2. y+ 10 ≤ 12


2. − 6 x≥ 30 4. −x< 8


3. 7 < 2 y− 11 6. 14 − 6 x≥− 10

7.

y

2

− 1 > 4 8. 6 −

x

5

>− 14

CHALLENGE:Tim solved the inequality 4<− 3 x−2. He found that 6<− 3 x

and that− 2 >x. The correct answer on his teacher’s answer key was

x<−2. Was Tim also correct? Explain your answer.

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Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.