# Linear Inequalities in One Variable

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 3x ≤ 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