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# 1.5 Solving Linear Inequalities - PowerPoint PPT Presentation

1.5 Solving Linear Inequalities. Inequality Symbols. Less than. Not equal to. Less than or equal to. Greater than or equal to. Greater than. Inequality with one variable to the first power. for example: 2x-3<8 A solution is a value of the variable that makes the inequality true.

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### 1.5 Solving Linear Inequalities

Less than

Not equal to

Less than or equal to

Greater than or equal to

Greater than

Linear Inequality

Transformations for Inequalities

2x-3<8

+3 +3

2x<11

2 2

x<

Flip the sign after dividing by the -3!

• Remember:

< and > signs will have an open dot o

and signs will have a closed dot

graph of graph of

Graphing Linear Inequalities

4

5

6

7

-3

-2

-1

0

Example: Solve and graph the solution.

6

7

8

9

Compound Inequality

-3 -2 -1 0 1 2 3 4 5

-4 -3 -2 -1 0 1 2

-13 < t < 6

Think between!

Example: Solve & graph.

-13

6

-6x < -6 -3x > 21

x > 1 or x < -7

Flip signs

Think oars

Last example! Solve & graph.

-7

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