Function Basic: Background You’ll Need 2

Giselle Miller

Function Basic: Background You’ll Need 2

Calculate an algebraic expression using given numbers for the variables

Algebraic Expressions

An algebraic expression is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division. For example, [latex]3x + 2y - 7[/latex] is an algebraic expression that contains two variables [latex]x[/latex] and [latex]y[/latex] and three constants [latex]3[/latex], [latex]2[/latex], and [latex]7[/latex].

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.

How To: Evaluate Algebraic ExpressionsUse the following steps to evaluate an algebraic expression:

Replace each variable in the expression with the given value
Simplify the resulting expression using the order of operations

Note: If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.

Evaluate each expression for the given values.

[latex]x+5[/latex] for [latex]x=-5[/latex]

Substitute [latex]-5[/latex] for [latex]x[/latex].

[latex]\begin{align}x+5 &=\left(-5\right)+5 \\ &=0\end{align}[/latex]
[latex]\dfrac{t}{2t - 1}[/latex] for [latex]t=10[/latex]

Substitute [latex]10[/latex] for [latex]t[/latex].

[latex]\begin{align}\dfrac{t}{2t-1} & =\dfrac{\left(10\right)}{2\left(10\right)-1} \\ & =\dfrac{10}{20-1} \\ & =\dfrac{10}{19}\end{align}[/latex]
[latex]\dfrac{4}{3}\pi {r}^{3}[/latex] for [latex]r=5[/latex]

Substitute [latex]5[/latex] for [latex]r[/latex].

[latex]\begin{align}\frac{4}{3}\pi r^{3} & =\frac{4}{3}\pi\left(5\right)^{3} \\ & =\frac{4}{3}\pi\left(125\right) \\ & =\frac{500}{3}\pi\end{align}[/latex]
[latex]a+ab+b[/latex] for [latex]a=11,b=-8[/latex]

Substitute [latex]11[/latex] for [latex]a[/latex] and –8 for [latex]b[/latex].

[latex]\begin{align}a+ab+b & =\left(11\right)+\left(11\right)\left(-8\right)+\left(-8\right) \\ & =11-8-8 \\ & =-85\end{align}[/latex]
[latex]\sqrt{2{m}^{3}{n}^{2}}[/latex] for [latex]m=2,n=3[/latex]

Substitute [latex]2[/latex] for [latex]m[/latex] and [latex]3[/latex] for [latex]n[/latex].

[latex]\begin{align}\sqrt{2m^{3}n^{2}} & =\sqrt{2\left(2\right)^{3}\left(3\right)^{2}} \\ & =\sqrt{2\left(8\right)\left(9\right)} \\ & =\sqrt{144} \\ & =12\end{align}[/latex]