/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 8.124 Solve:聽32b+3-25=50... [FREE SOLUTION] | 91影视

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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. 8.124 (page 818)

Solve: $3 \sqrt{2 b + 3} - 25 = 50$

Short Answer

Expert verified

The solution is $b = 311$ .

Step by step solution

01

Step 1. Isolate the radical

Consider the equation $3 \sqrt{2 b + 3} - 25 = 50$ .

In the equation, isolate the radical by first adding $25$ both sides.

role="math" localid="1644861223972" $\begin{array}{rcl} 3 \sqrt{2 b + 3} - 25 + 25 & = & 50 + 25 \\ 3 \sqrt{2 b + 3} & = & 75 \end{array}$

Now divide both sides by $3$ .

$\begin{array}{rcl} \frac{3 \sqrt{2 b + 3}}{3} & = & \frac{75}{3} \\ \sqrt{2 b + 3} & = & 25 \end{array}$

02

Step 2. Square both sides and solve for b

Remove the radical by squaring both sides.

$\begin{array}{rcl} {(\sqrt{2 b + 3})}^{2} & = & 25^{2} \\ 2 b + 3 & = & 625 \end{array}$

Subtract $3$ from both sides

$\begin{array}{rcl} 2 b + 3 - 3 & = & 625 - 3 \\ 2 b & = & 622 \end{array}$

Now divide both sides by $2$ and solve for $b$ .

$\begin{array}{rcl} \frac{2 b}{2} & = & \frac{622}{2} \\ b & = & 311 \end{array}$

03

Step 3. Check the solution

Substitute $311$ for $b$ in the given equation.

$\begin{array}{rcl} 3 \sqrt{2 b + 3} - 25 & = & 50 \\ 3 \sqrt{2 路 311 + 3} - 25 & = & 50 \\ 3 \sqrt{622 + 3} - 25 & = & 50 \\ 3 \sqrt{625} - 25 & = & 50 \\ 3 路 25 - 25 & = & 50 \\ 75 - 25 & = & 50 \\ 50 & = & 50 \end{array}$

So, we get a true statement. Thus the solution found is correct.

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[4]{3125}$ , b. $\sqrt[3]{81}$

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