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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. 307 (page 824)

In the following exercises, solve.
$\sqrt[3]{4 x + 5} - 2 = - 5$

Short Answer

Expert verified

The solution of the given equation is $x = - 8$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$\sqrt[3]{4 x + 5} - 2 = - 5$

02

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl} \sqrt[3]{4 x + 5} & = & - 5 + 2 \\ \sqrt[3]{4 x + 5} & = & - 3 \end{array}$

Take cube on both sides.

$\begin{array}{rcl} (\sqrt[3]{4 x + 5})^{3} & = & (- 3)^{3} \\ 4 x + 5 & = & - 27 \\ 4 x & = & - 27 - 5 \\ 4 x & = & - 32 \end{array}$

Divide both sides by 4.

$\begin{array}{rcl} \frac{4 x}{4} & = & \frac{- 32}{4} \\ x & = & - 8 \end{array}$

03

Step 3. Conclusion.

The solution of the given equation is $x = - 8$ .

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{9}}{s^{8}}}$

(b) $\sqrt[3]{\frac{54 a^{8}}{b^{3}}}$

(c) $\sqrt[4]{\frac{64 c^{5}}{d^{4}}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{6} s^{8}}{48 r s^{4}}}$

(b) $\sqrt[3]{\frac{24 x^{8} y 4}{81 x^{2} y}}$

(c) $\sqrt[4]{\frac{32 m^{9} n^{2}}{162 m n^{2}}}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{147}$

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

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