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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 2.144 (page 202)

Solve: $|6 x - 5| = |3 x + 4|$

Short Answer

Expert verified

The required solutions are $x_{1} = \frac{1}{9}, 鈥� x_{2} = 3$ .

Step by step solution

01

Step 1. Given information.

We have:

$|6 x - 5| = |3 x + 4|$

02

Step 2. Write the equivalent equations.

We have:

$|6 x - 5| = |3 x + 4|$

Write the inequality as $(6 x - 5) = - (3 x + 4)$ or $(6 x - 5) = (3 x + 4)$ .

03

Step 3. Solve the each equations.

Start with first equation:

$(6 x - 5) = - (3 x + 4)$

$6 x - 5 = - 3 x - 4 6 x - 5 + 5 = - 3 x - 4 + 5 6 x = - 3 x + 1 6 x + 3 x = - 3 x + 1 + 3 x 9 x = 1 x = \frac{1}{9}$

Now, solve the second equation:

$(6 x - 5) = (3 x + 4)$

$6 x - 5 + 5 = 3 x + 4 + 5 6 x = 3 x + 9 6 x - 3 x = 3 x + 9 - 3 x 3 x = 9 \frac{3 x}{3} = \frac{9}{3} x = 3$

04

Step 4. Check the each solution.

Substitute $\frac{1}{9}$ and $3$ into the original equation:

$|6 x - 5| = |3 x + 4|$

At $x = \frac{1}{9}$ :

$|6 (\frac{1}{9}) - 5| = |3 (\frac{1}{9}) + 4| \frac{13}{3} = \frac{13}{3}$

At $x = 3 :$

$|6 (3) - 5| = |3 (3) + 4| 13 = 13$

Hence, verified.

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