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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. 308 (page 824)

In the following exercises, solve.
$\sqrt[3]{9 x - 1} - 1 = - 5$

Short Answer

Expert verified

The solution of the given equation is $x = - 7$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$\sqrt[3]{9 x - 1} - 1 = - 5$

02

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl} \sqrt[3]{9 x - 1} & = & - 5 + 1 \\ \sqrt[3]{9 x - 1} & = & - 4 \end{array}$

Take cube on both sides.

$\begin{array}{rcl} (\sqrt[3]{9 x - 1})^{3} & = & (- 4)^{3} \\ 9 x - 1 & = & - 64 \\ 9 x & = & - 64 + 1 \\ 9 x & = & - 63 \end{array}$

Divide both sides by 9.

$\begin{array}{rcl} \frac{9 x}{9} & = & \frac{- 63}{9} \\ x & = & - 7 \end{array}$

03

Step 3. Conclusion.

The solution of the given equation is $x = - 7$ .

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{800}$

Simplify:

a. $y^{\frac{3}{4}} 路 y^{\frac{5}{8}}$ b. ${(m^{9})}^{\frac{2}{9}}$ c. $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

Simplify:

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

In the following exercises, simplify using absolute value signs as needed. $\sqrt{147 m^{7} n^{11}}, \sqrt[3]{48 x^{6} y^{7}}, \sqrt[4]{32 x^{5} y^{4}}$

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