Inequalities and Compound Inequalities

Info: A solution to an inequality in one variable is a value of the variable that makes the inequality true. The graph of an inequality in one variable consists of all points on a real number line that correspond to solutions of the inequality.

Inequalities

Variable on one side

Solve: 2x + 7 17

2x 10 – Subtract 7 from each side

x 5 – Divide each side by 2

-10 -5 0 5 10

Variable on both sides

Solve: 10x + 2 8x – 16

2x + 2  -16 – Subtract 8x from each side

2x -18 – Subtract 2 from each side

x -9 – Divide each side by 2

-10 -5 0 5 10

Compound Inequalities

An “and” Inequality- To solve you have to separate the variable, which is X, between the two inequality numbers.

Solve:-9 2x – 5 5

-4 2x 10 - Add 5 to each expression

-2 x 5 - Divide each expression by 2

-10 -5 0 5 10

An “or” Inequality- To solve you must break up the problems and do the each separately as you would do regularly.

Solve: 3x + 6 18 or 4x - 7  -3

1^st Part 2^nd Part

3x 12 – Subtract 6 from each side 4x   4 – Add 7 to each side

x 4 - Divide each side by 3 x   1 – Divide each side by 4

-10 -5 0 5 10

Practice Problems

1. 6x - 2  10

2. 9x - 3  2x +18

3. -4  4x + 4  24

4. 3x + 3  -6 or 5x - 4  21