Read: Evaluate Algebraic Expressions
Learning Objectives
- Define and identify constants in an algebraic expression
- Evaluate algebraic expressions for different values
In each case, the exponent tells us how many factors of the base to use, whether the base consists of constants or variables.
In the following example, we will practice identifying constants and variables in mathematical expressions.
Example
List the constants and variables for each algebraic expression.Answer:
Expression | Constants | Variables |
---|---|---|
1. | ||
2. | ||
3. |
Example
Evaluate the expression for each value for .Answer:
- Substitute 0 for .
\begin{array}\text{ }2x-7 \hfill& = 2\left(0\right)-7 \\ \hfill& =0-7 \\ \hfill& =-7\end{array}
- Substitute 1 for .
\begin{array}\text{ }2x-7 \hfill& = 2\left(1\right)-7 \\ \hfill& =2-7 \\ \hfill& =-5\end{array}
- Substitute for .
\begin{array}\text{ }2x-7 \hfill& = 2\left(\frac{1}{2}\right)-7 \\ \hfill& =1-7 \\ \hfill& =-6\end{array}
- Substitute for .
\begin{array}\text{ }2x-7 \hfill& = 2\left(-4\right)-7 \\ \hfill& =-8-7 \\ \hfill& =-15\end{array}
Example
Evaluate each expression for the given values.- for
- for
- for
- for
- for
Answer:
- Substitute for .
\begin{array}\text{ }x+5\hfill&=\left(-5\right)+5 \\ \hfill&=0\end{array}
- Substitute 10 for .
\begin{array}\text{ }\frac{t}{2t-1}\hfill& =\frac{\left(10\right)}{2\left(10\right)-1} \\ \hfill& =\frac{10}{20-1} \\ \hfill& =\frac{10}{19}\end{array}
- Substitute 5 for .
\begin{array}\text{ }\frac{4}{3}\pi r^{3} \hfill& =\frac{4}{3}\pi\left(5\right)^{3} \\ \hfill& =\frac{4}{3}\pi\left(125\right) \\ \hfill& =\frac{500}{3}\pi\end{array}
- Substitute 11 for and –8 for .
\begin{array}\text{ }a+ab+b \hfill& =\left(11\right)+\left(11\right)\left(-8\right)+\left(-8\right) \\ \hfill& =11-88-8 \\ \hfill& =-85\end{array}
- Substitute 2 for and 3 for .
\begin{array}\text{ }\sqrt{2m^{3}n^{2}} \hfill& =\sqrt{2\left(2\right)^{3}\left(3\right)^{2}} \\ \hfill& =\sqrt{2\left(8\right)\left(9\right)} \\ \hfill& =\sqrt{144} \\ \hfill& =12\end{array}