1.5 Solving Linear Inequalities

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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&lt;8 A solution is a value of the variable that makes the inequality true.

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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.

x could equal -3, 0, 1, etc.

Linear Inequality

Add/subtract the same number on each side of an inequality

• Multiply/divide by the same positive number on each side of an inequality
• If you multiply or divide by a negative number, you MUSTflip the inequality sign!
Transformations for Inequalities
Ex: Solve the inequality.

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

An inequality joined by “and” or “or”.

Examples

“and” “or”

think between

think oars on a boat

Compound Inequality

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

-4 -3 -2 -1 0 1 2

-9 < t+4 < 10

-13 < t < 6

Think between!

Example: Solve & graph.

-13

6

-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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