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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. 298 (page 824)

In the following exercises, solve.
$\sqrt{6 n + 1} + 4 = 8$

Short Answer

Expert verified

The solution of the given equation is $n = 2.5$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$\sqrt{6 n + 1} + 4 = 8$

02

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl} \sqrt{6 n + 1} & = & 8 - 4 \\ \sqrt{6 n + 1} & = & 4 \end{array}$

Take square on both sides.

$\begin{array}{rcl} (\sqrt{6 n + 1})^{2} & = & (4)^{2} \\ 6 n + 1 & = & 16 \\ 6 n & = & 16 - 1 \\ 6 n & = & 15 \end{array}$

Divide both sides by 6.

$\begin{array}{rcl} \frac{6 n}{6} & = & \frac{15}{6} \\ n & = & 2.5 \end{array}$

03

Step 3. Conclusion.

The solution of the given equation is $n = 2.5$ .

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Simplify:

a. $\frac{u^{\frac{4}{5}} 路 u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$

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