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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 444 (page 208)

In the following exercises, solve.
$3 |4 x - 5| - 4 = 11$

Short Answer

Expert verified

The solution is $x = 0$ or $x = \frac{5}{2}$

Step by step solution

01

Step 1. Given information

Absolute value equation: $3 |4 x - 5| - 4 = 11$

02

Step 2. Calculation

We have,

$3 |4 x - 5| - 4 = 11$

$3 |4 x - 5| - 4 + 4 = 11 + 4$

$3 |4 x - 5| = 15$

$\frac{3 |4 x - 5|}{3} = \frac{15}{3}$

$|4 x - 5| = 5$

$4 x - 5 = - 5$ or $4 x - 5 = 5$

$4 x - 5 + 5 = - 5 + 5$ or $4 x - 5 + 5 = 5 + 5$

$4 x = 0$ or $4 x = 10$

$\frac{4 x}{4} = \frac{0}{4}$ or $\frac{4 x}{4} = \frac{10}{4}$

$x = 0$ or $x = \frac{5}{2}$

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