# Evaluating Variable Expressions with Integers

## Evaluating Variable Expressions with Integers

Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions.

## Example

Evaluate $$x+7\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}$$

1. $$\phantom{\rule{0.2em}{0ex}}x=-2\phantom{\rule{0.2em}{0ex}}$$
2. $$\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}x=-11.$$

### Solution

 Evaluate $$x+7$$ when $$x=-2$$ Simplify.
 Evaluate $$x+7$$ when $$x=-11$$ Simplify.

## Example

When $$n=-5,$$ evaluate 

1. $$\phantom{\rule{0.2em}{0ex}}n+1\phantom{\rule{0.2em}{0ex}}$$
2. $$\phantom{\rule{0.2em}{0ex}}-n+1.$$

### Solution

 Evaluate $$n+1$$ when $$n=-5$$ Simplify.
 Evaluate $$-n+1$$ when $$n=-5$$ Simplify. Add.

Next we’ll evaluate an expression with two variables.

## Example

Evaluate $$3a+b$$ when $$a=12$$ and $$b=-30.$$

## Example

Evaluate $${\left(x+y\right)}^{2}$$ when $$x=-18$$ and $$y=24.$$

### Solution

This expression has two variables. Substitute $$-18$$ for $$x$$ and $$24$$ for $$y.$$

 $${\left(x+y\right)}^{2}$$ $${\left(-18+24\right)}^{2}$$ Add inside the parentheses. $${\left(6\right)}^{2}$$ Simplify $$36$$