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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

1.5 Solving Linear Inequalities


Inequality symbols
Inequality Symbols

Less than

Not equal to

Less than or equal to

Greater than or equal to

Greater than


Linear inequality

Linear Inequality


Transformations for inequalities

Transformations for Inequalities


Ex solve the inequality
Ex: Solve the inequality.

2x-3<8

+3 +3

2x<11

2 2

x<

Flip the sign after dividing by the -3!


Graphing linear inequalities

  • 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
Example: Solve and graph the solution.

6

7

8

9


Compound inequality

Compound Inequality

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

-4 -3 -2 -1 0 1 2


Example solve graph

-9 < t+4 < 10

-13 < t < 6

Think between!

Example: Solve & graph.

-13

6


Last example solve graph

-6x+9 < 3 or -3x-8 > 13

-6x < -6 -3x > 21

x > 1 or x < -7

Flip signs

Think oars

Last example! Solve & graph.

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