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

**Multiplication Property of Inequality**

For all real numbers *A*, *B*, and *C*, with *C *Z 0,

**(a)** the inequalities

*A *< *B *and *AC *< *BC*

are equivalent if *C *> 0;

**(b)** the inequalities

*A *< *B *and *AC *> *BC*

are equivalent if *C *< 0.

In words, each side of an inequality may be multiplied (or divided)

by a *positive *number without changing the direction of the inequality

symbol. *Multiplying (or dividing) by a negative number requires that*

*we reverse the inequality symbol*.