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. $x=1$

Answer: Solution Remember $ab$ means $a$ times $b$, so $9x$ means $9$ times $x$. 1. To evaluate the expression when $x=5$, we substitute $5$ for $x$, and then simplify.

	$9x-2$
Substitute $\color{red}{5}$ for x.	$9\cdot\color{red}{5}-2$
Multiply.	$45-2$
Subtract.	$43$

2. To evaluate the expression when $x=1$, we substitute $1$ for $x$, and then simplify.

	$9x-2$
Substitute $\color{red}{1}$ for x.	$9(\color{red}{1})-2$
Multiply.	$9-2$
Subtract.	$7$

Notice that in part 1 that we wrote $9\cdot 5$ and in part 2 we wrote $9\left(1\right)$. Both the dot and the parentheses tell us to multiply.

example

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

Answer: Solution We substitute $10$ for $x$, and then simplify the expression.

	$x^2$
Substitute $\color{red}{10}$ for x.	${\color{red}{10}}^{2}$
Use the definition of exponent.	$10\cdot 10$
Multiply.	$100$

When $x=10$, the expression ${x}^{2}$ has a value of $100$.

example

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

Answer: Solution In this expression, the variable is an exponent.

	$2^x$
Substitute $\color{red}{5}$ for x.	${2}^{\color{red}{5}}$
Use the definition of exponent.	$2\cdot2\cdot2\cdot2\cdot2$
Multiply.	$32$

When $x=5$, the expression ${2}^{x}$ has a value of $32$.

example

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

Answer: Solution   This expression contains two variables, so we must make two substitutions.

	$3x+4y-6$
Substitute $\color{red}{10}$ for x and $\color{blue}{2}$ for y.	$3(\color{red}{10})+4(\color{blue}{2})-6$
Multiply.	$30+8-6$
Add and subtract left to right.	$32$

When $x=10$ and $y=2$, the expression $3x+4y - 6$ has a value of $32$.

example

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

Answer: Solution We need to be careful when an expression has a variable with an exponent. In this expression, $2{x}^{2}$ means $2\cdot x\cdot x$ and is different from the expression ${\left(2x\right)}^{2}$, which means $2x\cdot 2x$.

	$2x^2+3x+8$
Substitute $\color{red}{4}$ for each x.	$2{(\color{red}{4})}^{2}+3(\color{red}{4})+8$
Simplify ${4}^{2}$ .	$2(16)+3(4)+8$
Multiply.	$32+12+8$
Add.	$52$