Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - Chapter Review - Page 425: 46



Work Step by Step

Divide $5$ to both sides: \begin{align*} \dfrac{5(3x+1)^{\frac{1}{4}}}{5}&=\dfrac{10}{5}\\\\ (3x+1)^{\frac{1}{4}}&=2\\ \end{align*} Raise both sides to the fourth power: \begin{align*} \left[(3x+1)^{\frac{1}{4}}\right]^4=2^4\\\\ 3x+1&=16\\ \end{align*} Solve for $x$: \begin{align*} 3x&=16-1\\\\ 3x&=15\\\\ \frac{3x}{3}&=\frac{15}{3}\\\\ x&=5 \end{align*}
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