Evaluating Algebraic Expressions

Learning Outcomes

• Evaluate an expression for a given value

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.

To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

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. $x=1$

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.