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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 450 (page 208)

In the following exercises, solve.
$|\frac{1}{2} x + 5| + 4 = 1$

Short Answer

Expert verified

The solution is $x = - 16 o r x = - 4$

Step by step solution

01

Step 1. Given information

Absolute value equation: $|\frac{1}{2} x + 5| + 4 = 1$

02

Step 2. Calculation

We have,

$|\frac{1}{2} x + 5| + 4 = 1$

$|\frac{1}{2} x + 5| + 4 - 4 = 1 - 4$

$|\frac{1}{2} x + 5| = - 3 \frac{1}{2} x + 5 = - 3 o r \frac{1}{2} x + 5 = 3$

$\frac{1}{2} x + 5 - 5 = - 3 - 5 o r \frac{1}{2} x + 5 - 5 = 3 - 5 \frac{1}{2} x = - 8 o r \frac{1}{2} x = - 2$

$\frac{1}{2} x \times 2 = - 8 \times 2 o r \frac{1}{2} x \times 2 = - 2 \times 2 x = - 16 o r x = - 4$

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