example

Evaluate [latex]x+7[/latex] when

1. [latex]x=3[/latex]
2. [latex]x=12[/latex]

Solution: 1. To evaluate, substitute [latex]3[/latex] for [latex]x[/latex] in the expression, and then simplify.

	[latex]x+7[/latex]
Substitute.	[latex]\color{red}{3}+7[/latex]
Add.	[latex]10[/latex]

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

	[latex]x+7[/latex]
Substitute.	[latex]\color{red}{12}+7[/latex]
Add.	[latex]19[/latex]

When [latex]x=12[/latex], the expression [latex]x+7[/latex] has a value of [latex]19[/latex]. 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 [latex]x[/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.

example

Evaluate [latex]9x - 2,[/latex] when

1. [latex]x=5[/latex]
2. [latex]x=1[/latex]

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

	[latex]9x-2[/latex]
Substitute [latex]\color{red}{5}[/latex] for x.	[latex]9\cdot\color{red}{5}-2[/latex]
Multiply.	[latex]45-2[/latex]
Subtract.	[latex]43[/latex]

2. To evaluate the expression when [latex]x=1[/latex], we substitute [latex]1[/latex] for [latex]x[/latex], and then simplify.

	[latex]9x-2[/latex]
Substitute [latex]\color{red}{1}[/latex] for x.	[latex]9(\color{red}{1})-2[/latex]
Multiply.	[latex]9-2[/latex]
Subtract.	[latex]7[/latex]

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

example

Evaluate [latex]{x}^{2}[/latex] when [latex]x=10[/latex].

Answer: Solution We substitute [latex]10[/latex] for [latex]x[/latex], and then simplify the expression.

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

When [latex]x=10[/latex], the expression [latex]{x}^{2}[/latex] has a value of [latex]100[/latex].

example

[latex]\text{Evaluate }{2}^{x}\text{ when }x=5[/latex].

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

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

When [latex]x=5[/latex], the expression [latex]{2}^{x}[/latex] has a value of [latex]32[/latex].

example

[latex]\text{Evaluate }3x+4y - 6\text{ when }x=10\text{ and }y=2[/latex].

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

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

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

example

[latex]\text{Evaluate }2{x}^{2}+3x+8\text{ when }x=4[/latex].

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

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