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Exercises Expressions, exponents and radicals

Example 10 from Algebra and Trigonometry, 1.1 Real Numbers: Algebra Essentials

Evaluating Algebraic Expressions

Evaluate each expression for the given values.

ⓐ $x + 5$ for $x = −5$
ⓑ $\frac{t}{2 t −1}$ for $t = 10$
ⓒ $\frac{4}{3} π r^{3}$ for $r = 5$
ⓓ $a + a b + b$ for $a = 11, b = −8$
ⓔ $\sqrt{2 m^{3} n^{2}}$ for $m = 2, n = 3$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ Substitute $−5$ for $x .$
  $\begin{matrix} x + 5 & = & (−5) + 5 \\ = & 0 \end{matrix}$
2. ⓑ Substitute 10 for $t .$
  $\begin{matrix} \frac{t}{2 t - 1} & = & \frac{(10)}{2 (10) - 1} \\ = & \frac{10}{20 - 1} \\ = & \frac{10}{19} \end{matrix}$
3. ⓒ Substitute 5 for $r .$
  $\begin{matrix} \frac{4}{3} π r^{3} & = & \frac{4}{3} π {(5)}^{3} \\ = & \frac{4}{3} π (125) \\ = & \frac{500}{3} π \end{matrix}$
4. ⓓ Substitute 11 for $a$ and –8 for $b .$
  $\begin{matrix} a + a b + b & = & (11) + (11) (−8) + (−8) \\ = & 11 - 88 - 8 \\ = & −85 \end{matrix}$
5. ⓔ Substitute 2 for $m$ and 3 for $n .$
  $\begin{matrix} \sqrt{2 m^{3} n^{2}} & = & \sqrt{2 {(2)}^{3} {(3)}^{2}} \\ = & \sqrt{2 (8) (9)} \\ = & \sqrt{144} \\ = & 12 \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Evaluate each expression for the given values.

ⓐ $\frac{y + 3}{y - 3}$ for $y = 5$
ⓑ $7 - 2 t$ for $t = −2$
ⓒ $\frac{1}{3} π r^{2}$ for $r = 11$
ⓓ ${(p^{2} q)}^{3}$ for $p = −2, q = 3$
ⓔ $4 (m - n) - 5 (n - m)$ for $m = \frac{2}{3}, n = \frac{1}{3}$

How did it go?

PreviousEvaluating an Algebraic Expression at Different Values Next Using a Formula

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.