## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 7 - Section 7.6 - Radical Equations - Exercise Set: 38

#### Answer

$x=3$

#### Work Step by Step

RECALL: For any non-negative real number $a$, $\left(a^{\frac{1}{4}}\right)^4=a$ Raise both sides of the equation to the fourth power then sue the rule above to simplify. $\left((x-2)^{\frac{1}{4}}\right)^4=\left((3x-8)^{\frac{1}{4}}\right)^4 \\x-2=3x-8$ Subtract $x$ and add $8$ on both sides of the equation to obtain: $-2+8=3x-x 6=2x$ Divide 2 on both sides to obtain: $3=x$

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