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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 448 (page 208)

In the following exercise, solve.
$|\frac{3}{4} x - 3| + 7 = 2$

Short Answer

Expert verified

The solution is $x = - \frac{8}{3} o r x = \frac{32}{3}$

Step by step solution

01

Step 1. Given information

Absolute value equation: $|\frac{3}{4} x - 3| + 7 = 2$

02

Step 2. Calculation

We have,

$|\frac{3}{4} x - 3| + 7 = 2$

$|\frac{3}{4} x - 3| + 7 - 7 = 2 - 7$

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

$\frac{3}{4} x - 3 = - 5 o r \frac{3}{4} x - 3 = 5$

$\frac{3}{4} x - 3 + 3 = - 5 + 3 o r \frac{3}{4} x - 3 + 3 = 5 + 3$

$\frac{3}{4} x = - 2 o r \frac{3}{4} x = 8 \frac{3}{4} x \times 4 = - 2 \times 4 o r \frac{3}{4} x \times 4 = 8 \times 4$

$3 x = - 8 o r 3 x = 32 \frac{3 x}{3} = \frac{- 8}{3} o r \frac{3 x}{3} = \frac{32}{3} x = - \frac{8}{3} o r x = \frac{32}{3}$

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Most popular questions from this chapter

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See all solutions

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