5.1 Algebraic Expressions

5.3 Linear Inequalities in One Variable with Applications

For any numbers $a$ , $b$ , and $,$ if $a < b$ , then $a + c < b + c$ and $a - c < b - c$ .
For any numbers $a$ , $b$ , and $c$ , if $a > b$ , then $a + c > b + c$ and $a - c > b - c$ .
For any numbers $a$ , $b$ , and $c$ ,
multiply or divide by a positive:
if $a < b$ and $c > 0$ , then $a c < b c$ and $\frac{a}{c} < \frac{b}{c}$
if $a > b$ and $c > 0$ , then $a c > b c$ and $\frac{a}{c} > \frac{b}{c}$
multiply or divide by a negative:
if $a < b$ and $c < 0$ , then $a c > b c$ and $\frac{a}{c} > \frac{b}{c}$
if $a > b$ and $c < 0$ , then $a c < b c$ and $\frac{a}{c} < \frac{b}{c}$

To calculate slope $(m)$ , use the formula
$m = \frac{r i s e}{r u n}$ ,
where the rise measures the vertical change and the run measures the horizontal change.
To find the slope of the line between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ , use the formula
$m = \frac{y 2 - y 1}{x 2 - x 1}$