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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 306 (page 982)

In the following exercises, solve.
$\frac{6}{3} - \frac{2}{d} = \frac{4}{9}$

Short Answer

Expert verified

The solution of the equation $\frac{6}{3} - \frac{2}{d} = \frac{4}{9}$ is

$d = \frac{9}{7}$

Step by step solution

01

Step 1. Given information

The given equation is

$\frac{6}{3} - \frac{2}{d} = \frac{4}{9}$

02

Step 2. Solution of equation

In the equation, the term $\frac{2}{d}$ is undefined for $d = 0$

sorole="math" localid="1647784110699" $\frac{6}{3} - \frac{2}{d} = \frac{4}{9}, d 鈮� 0$

the least common denominator of all denominators in the equation is $9 d$

multiply both sides of the equation by the least common denominator $9 d$

$9 d (\frac{6}{3} - \frac{2}{d}) = 9 d (\frac{4}{9}) 9 d (\frac{6}{3}) - 9 d (\frac{2}{d}) = 9 d (\frac{4}{9}) 18 d - 18 = 4 d 14 d = 18 d = \frac{18}{14} d = \frac{9}{7}$

So the solution of the equation is $d = \frac{9}{7}$

03

Step 3. Verification

Substitute $d = \frac{9}{7}$ in the equation

$\frac{6}{3} - \frac{2}{d} = \frac{4}{9} \frac{6}{3} - \frac{2}{\frac{9}{7}} \overset{?}{=} \frac{4}{9} \frac{18}{9} - \frac{14}{9} \overset{?}{=} \frac{4}{9} \frac{4}{9} = \frac{4}{9}$

The left-hand side is equal to the right-hand side so the solution is correct.

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