# Evaluating Expressions

Expressions are different from equations in that they don't have equal signs. The contain variables, but because they are not equal to anything, you can't solve for the variable.

However, sometimes you will be asked to evaluate expressions when you are given the value of the variable (or several variables).

Variables just stand for numbers, so if you are given values of variables, just replace the variables with the numbers. It can help to put the number into the expression surrounded by paratheses so that you remember that a term like $3x$ is the same as $3\times x$ so if $x=4$ then $3x=3(4)=12$. If you don't put the parentheses in, there a possibility that you get confused and think that $3x=34$. The parentheses help prevent that from happening.

*Example*:

Evaluate the following expression: $x^2+5x+2$ if $x=2$

Take the $x$s and replace them with $2$ throughout the expression. Don't forget the parentheses.

If $x=2$, then $x^2+5x+2=(2)^2+5(2)+2=4+10+2=16$

Sometimes you will be given the values of several variables.

*Example*:

Evaluate the following expression: $x^2+9x-3y+7$ if $x=4$ and $y=2$

Take the $x$s and $y$s and replace them with$4$ and $2$ throughout the expression. Don't forget the parentheses.

If $x=4$ and $y=2$, then $x^2+9x-3y+7=(4)^2+9(4)-3(2)+7=16+36-6+7=53$

Overall, evaluating expressions is just a matter of plugging values in for variables and solving!

#### Practice Problems:

## Evaluating Expressions

Evaluate the following expressions.

1. $x-13$ when $x=17$

2. $23+x$ when $x=3$

3. $18.9+x$ when $x=2.31$

4. $3x^2-4x+5$ when $x=2$

5. $x^3+2x^2+3x-7$ when $x=7$

6. $\dfrac{2}{x}+\dfrac{5}{2x}$ when $x=3$

7. $4-3\dfrac{3}{x}$ when $x=4$

8. $\dfrac{9+x}{10x-4}$ when $x=5$

9. $\dfrac{14}{38}x$ when $x=\dfrac{19}{54}$

10. $3x+7y^2+2y$ when $x=12$ and $y=11$

11. $13x-21y+37z-8$ when $x=23$, $y=1.5$, and $z=0.2$

12. $y^2+2y-3x^2+x^3-4x$ when $x=5$ and $y=9$

#### Answer Key: