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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.120 (page 816)

Solve: ${(4 x - 8)}^{\frac{1}{4}} + 5 = 7$ .

Short Answer

Expert verified

The solution is, $x = 6$ .

Step by step solution

01

Step 1 Given equation is,

${(4 x - 8)}^{\frac{1}{4}} + 5 = 7$ .

The objective is, we need to find the solution for the given equation.

02

Step 2 To isolate the radical, subtract 5 on both sides.

${(4 x - 8)}^{\frac{1}{4}} + 5 - 5 = 7 - 5 {(4 x - 8)}^{\frac{1}{4}} = 2$

Raise each side of the equation to fourth power.

${({(4 x - 8)}^{\frac{1}{4}})}^{4} = {(2)}^{4}$

Simplify it.

${({(4 x - 8)}^{\frac{1}{4}})}^{4} = {(2)}^{4} 4 x - 8 = 16 4 x = 16 + 8 4 x = 24 x = \frac{24}{4} x = 6$

03

Step 3 Let us check the answer.

Substitute $x = 6$ into the equation

${(4 x - 8)}^{\frac{1}{4}} + 5 = 7 {(4 (6) - 8)}^{\frac{1}{4}} + 5 = 7 {(24 - 8)}^{\frac{1}{4}} + 5 = 7 {(16)}^{\frac{1}{4}} + 5 = 7 {(2^{4})}^{\frac{1}{4}} + 5 = 7 2 + 5 = 7 7 = 7$

which is true.

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[4]{3125}$ , b. $\sqrt[3]{81}$

In the following exercises, simplify.

(a) $- 64^{\frac{3}{2}}$

(b) $- 64^{- \frac{3}{2}}$

(c) ${(- 64)}^{\frac{3}{2}}$

Simplify-

(a) $\sqrt{288}$

(b) $\sqrt[3]{81}$

(c) $\sqrt[4]{64}$

Simplify:

$(a) \sqrt[3]{- 64} (b) \sqrt[4]{- 81} .$

In the following exercises, write with a rational exponent.

$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

See all solutions

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