## Evaluating Algebraic Expressions

### Learning Outcomes

• Evaluate algebraic expressions for different values

## Evaluate Algebraic Expressions

In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations. We substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value then simplify the resulting expression using the order of operations. If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before. In the next example we show how to substitute various types of numbers into a mathematical expression.

### example

Evaluate $x+7$ when

1. $x=3$
2. $x=12$

Solution:

1. To evaluate, substitute $3$ for $x$ in the expression, and then simplify.

 $x+7$ Substitute. $\color{red}{3}+7$ Add. $10$

When $x=3$, the expression $x+7$ has a value of $10$.
2. To evaluate, substitute $12$ for $x$ in the expression, and then simplify.

 $x+7$ Substitute. $\color{red}{12}+7$ Add. $19$

When $x=12$, the expression $x+7$ has a value of $19$.

Notice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for $x$ were different. When we evaluate an expression, the value varies depending on the value used for the variable.

### example

Evaluate $9x - 2,$ when

1. $x=5$
2. $x=1$

### Exercises

Evaluate the expression $2x + 7$ for each value for $x$.

1. $x=0$
2. $x=1$

### example

Evaluate ${x}^{2}$ when $x=10$.

### example

$\text{Evaluate }{2}^{x}\text{ when }x=5$.

### example

$\text{Evaluate }3x+4y - 6\text{ when }x=10\text{ and }y=2$.

### example

$\text{Evaluate }2{x}^{2}+3x+8\text{ when }x=4$.

### try it

In the video below we show more examples of how to substitute a value for variable in an expression, then evaluate the expression.

Eventually you will be performing these operations on decimals, fractions, and negative numbers, so it is important that you get all the rules mastered with whole numbers first!