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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 8.119 (page 1069)

Solve: ${(9 x + 9)}^{\frac{1}{4}} - 2 = 1$

Short Answer

Expert verified

The solution is, $x = 8$

Step by step solution

01

Step 1 Given equation is,

${(9 x + 9)}^{\frac{1}{4}} - 2 = 1$ .

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

02

Step 2 To isolate the radical add 2 on both sides.

${(9 x + 9)}^{\frac{1}{4}} - 2 + 2 = 1 + 2 {(9 x + 9)}^{\frac{1}{4}} = 3$

Raise each side of the equation to the fourth power.

${({(9 x + 9)}^{\frac{1}{4}})}^{4} = {(3)}^{4}$

Simplify it.

${({(9 x + 9)}^{\frac{1}{4}})}^{4} = {(3)}^{4} 9 x + 9 = 81 9 x = 81 - 9 9 x = 72 x = \frac{72}{9} x = 8$

03

Step 3 Let us check the answer.

Substitute $x = 8$ into the equation ${(9 x + 9)}^{\frac{1}{4}} - 2 = 1$ .

${(9 (8) + 9)}^{\frac{1}{4}} - 2 = 1 {(72 + 9)}^{\frac{1}{4}} - 2 = 1 {(81)}^{\frac{1}{4}} - 2 = 1 {(3^{4})}^{\frac{1}{4}} - 2 = 1 3 - 2 = 1 1 = 1$

which is true.

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Most popular questions from this chapter

In the following exercises, factor completely using the difference of squares pattern, if possible.

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