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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 245 (page 695)

Solve a Rational Equation for a Specific Variable.
In the following exercises, solve.
$\frac{m + 3}{n - 2} = \frac{4}{5}$ for $n$ .

Short Answer

Expert verified

The solution is $n = \frac{5 m + 23}{4}$ .

Step by step solution

01

Step 1. Given

The given rational equation is $\frac{m + 3}{n - 2} = \frac{4}{5}$ .

02

Step 2. To find

We have to solve the given rational equation for $n$ .

03

Step 3. Calculation

We cross multiply, then solve the equation for $n$ .

$\frac{m + 3}{n - 2} = \frac{4}{5} 5 (m + 3) = 4 (n - 2) 5 m + 15 = 4 n - 8 5 m + 15 + 8 = 4 n - 8 + 8 5 m + 23 = 4 n \frac{5 m + 23}{4} = \frac{4 n}{4} \frac{5 m + 23}{4} = n n = \frac{5 m + 23}{4}$

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