# Evaluating Expressions

Algebraic expressions are combinations of numbers, variables, and at least one arithmetic operation. To evaluate an algebraic expression for a given value, you have to substitute the known values of the variables and perform all the arithmetic operations of the expression using the correct order of operations. You might also not be given variables, in which case leave your answer in terms of the unknowns.

To make it easier to read as you are working with the expressions, you can put negative numbers inside parentheses.

## Evaluating expressions with one variable

The easiest expressions to evaluate are those with only one variable.

**Example 1**

Evaluate the expression

$4x+9$ for $x=2$

First, you have to replace the variable **x** with the value
**2**.

$4\left(2\right)+9$

Then you perform the multiplication, as the order of operations requires.

$8+9$

Finally, perform the addition.

$17$

So when $x=2,4x+9$ is evaluated as 17.

**Example 2**

Evaluate the expression ${x}^{2}-4x+1$ for $x=3$ .

To find the evaluation of the expression, we have to first substitute the variable x for the value 3.

${3}^{2}-4\left(3\right)+1$

Once we have substituted the value, we compute the operations. First, the power.

$9-4\left(3\right)+1$

Then the multiplication.

$9-12+1$

Then perform the addition and subtraction.

$-2$

So the evaluation of the expression ${x}^{2}-4x+1$ for $x=3$ is $-2$ .

## Evaluating expressions with more than one variable

Evaluating expressions with more than one variable is basically the same, only you have two variables to substitute with two values.

**Example 3**

Evaluate the expression $6(p+q)$ for $p=2$ and $q=-9$

To evaluate the expression, first substitute **2** for
**p** and **-9** for **q** in the expression.

$6\left(2+\left(-9\right)\right)$

Using the order of operations, simplify by performing the calculations in parentheses.

$6\left(-7\right)$

Now multiply 6 and -7.

$-42$

So, when **p** is **2** and **q** is **-9**, the value
of the expression is **-42**.

## Topics related to the Evaluating Expressions

Simplifying Rational Expressions

## Flashcards covering the Evaluating Expressions

## Practice tests covering the Evaluating Expressions

College Algebra Diagnostic Tests

## Get help learning about evaluating expressions

Evaluating expressions is one of the most important things your student can learn in algebra. If your student is having a difficult time learning to evaluate expressions, you might consider having them meet with an expert tutor. A tutor can complement your student's in-school learning by finding out their learning style and using customized teaching methods to match. Your student can ask questions as soon as they arise, making sure they are doing the problems correctly right from the beginning. If you want to know more about how tutoring can help your student learn the steps to evaluate expressions, contact the Educational Directors at Varsity Tutors today.

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