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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. 303 (page 982)

Solve Rational Equations
In the following exercises, solve.
$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ .

Short Answer

Expert verified

The solution for $a$ from the equation $\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ is, $a = 10$

Step by step solution

01

Step 1. Given information

$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ .

We need to solve the given equation.

02

Step 2.Note any value of the variable that would make any denominator zero.

$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}, a 鈮� 0$ .

Here, the LCD is, $10 a$ .

Multiply the given equation with LCD on both sides.

$10 a (\frac{1}{a} + \frac{2}{5}) = 10 a . \frac{1}{2}$

Distribute the LCD and then simplify it.

role="math" localid="1647850759521" $(\frac{10 a}{a} + \frac{20 a}{5}) = \frac{10 a}{2} 10 + 4 a = 5 a 5 a - 4 a = 10 a = 10$

03

Step 3. Let us check the answer.

Substitute $a = 10$ in the given equation.

$\frac{1}{a} + \frac{2}{5} = \frac{1}{2} \frac{1}{10} + \frac{2}{5} = \frac{1}{2} \frac{1 + 2 (2)}{10} = \frac{1}{2} \frac{1 + 4}{10} = \frac{1}{2} \frac{5}{10} = \frac{1}{2} \frac{1}{2} = \frac{1}{2}$

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Most popular questions from this chapter

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