**Linear Inequalities in One Variable**

**Linear Inequality**

** **

A linear inequality in one variable can be written in the form

Ax +B < c,

Where A,B, and C are real numbers, with A ≠ 0.

**Addition Property of Inequality**

For all real numbers *A*, *B*, and *C*, the inequalities

A < B and A + C < B+ C

Are equivalent.

In world, adding the same number to each side of an inequality does not change the solution set.

**Solve linear inequalities using the multiplication Property**

Solving an inequality such as 3*x *≤ 15 requires dividing each side by 3 using the multiplication property of inequality. To see how this property works, start with the true statement

-2 < 5.

Multiply each side by, say, 8.

-2(8) < 5(8) Multiply by 8.

-16 < 40 True

The result is true. Start again with -2 < 5, and multiply each side by -8.

-2 (-8) < 5(-8) Multiply by -8.

16 < -40 False

The result, 16 < -40, is false. To make it true, must change the direction of the inequality symbol to get

16 > -40. True