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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. 8.117 (page 815)

Solve: $\sqrt[3]{4 x - 3} + 8 = 5$ .

Short Answer

Expert verified

The solution is, $x = - 6$ .

Step by step solution

01

Step 1 Given equation is,

$\sqrt[3]{4 x - 3} + 8 = 5$ .

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

02

Step 2 To isolate the radical, subtract 8 on both sides.

$\sqrt[3]{4 x - 3} + 8 - 8 = 5 - 8 \sqrt[3]{4 x - 3} = - 3$

Now take cube on both sides.

$4 x - 3 = {(- 3)}^{3}$

Now simplify the above equation.

$4 x - 3 = - 27 4 x = - 27 + 3 4 x = - 24 x = \frac{- 24}{4} x = - 6$

03

Step 3 Let us check the answer.

Substitute $x = - 6$ into the equation. $\sqrt[3]{4 (- 6) - 3} + 8 = 5 \sqrt[3]{- 24 - 3} + 8 = 5 \sqrt[3]{- 27} + 8 = 5 \sqrt[3]{{(- 3)}^{3}} + 8 = 5 - 3 + 8 = 5 5 = 5$

which is true.

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Most popular questions from this chapter

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{98 r^{5}}{100}}$

In the following exercises, simplify.

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

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

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

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{45 r^{3}}{s^{10}}}$

(b) $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$

(c) $\sqrt[4]{\frac{729 c^{21}}{d^{8}}}$

Simplify:

$(a) 2 + \sqrt{98} (b) \frac{6 - \sqrt{45}}{3} .$

See all solutions

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