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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. 312 (page 824)

In the following exercises, solve.
$(12 x - 5)^{\frac{1}{3}} + 8 = 3$

Short Answer

Expert verified

The solution of the given equation is $x = - 10$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$(12 x - 5)^{\frac{1}{3}} + 8 = 3$

02

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl} (12 x - 5)^{\frac{1}{3}} & = & 3 - 8 \\ (12 x - 5)^{\frac{1}{3}} & = & - 5 \end{array}$

Take cube on both sides.

$\begin{array}{rcl} 12 x - 5 & = & (- 5)^{3} \\ 12 x & = & - 125 + 5 \\ x & = & \frac{- 120}{12} \\ x & = & - 10 \end{array}$

03

Step 3. Conclusion.

The solution of the given equation is $x = - 10$ .

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{96}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

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Explain the difference of finding the $n^{t h}$ root of a number when the index is even compared to when the index is odd.

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