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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 453 (page 208)

In the following exercises, solve.
$| 4 x + 3 | = | 2 x + 1 |$

Short Answer

Expert verified

The solution is $x = - 1 o r x = - \frac{2}{3}$

Step by step solution

01

Step 1. Given Information

Absolute value equation: $| 4 x + 3 | = | 2 x + 1 |$

02

Step 2. Calculation

We have,

$| 4 x + 3 | = | 2 x + 1 | 4 x + 3 = 2 x + 1 o r 4 x + 3 = - (2 x + 1) 4 x + 3 - 3 = 2 x + 1 - 3 o r 4 x + 3 - 3 = - 2 x - 1 - 3 4 x = 2 x - 2 o r 4 x = - 2 x - 4 4 x - 2 x = 2 x - 2 - 2 x o r 4 x + 2 x = - 2 x - 4 + 2 x 2 x = - 2 o r 6 x = - 4 x = \frac{- 2}{2} o r x = \frac{- 4}{6} x = - 1 o r x = - \frac{2}{3}$

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Most popular questions from this chapter

In the following exercises, solve each inequality, graph the solution in the number line and write the solution in interval notation.

$3 (2 x - 3) < - 5 o r 4 x - 1 > 3$

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