Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises: 12

Answer

$ \frac{2}{3} < x < 2 $

Work Step by Step

1. Get rid of the absolute value. Since the absolute value must be less than 2, what is inside the absolute value brackets must be between -2 and 2. So, $|3x - 4| \lt 2$ $-2 \lt 3x -4 \lt 2$ 2. Solve each side of the equation: $-2 \lt 3x -4$ $2 \lt 3x$ (Add 4 to each side) $\frac{2}{3} \lt x$ (divide each side by 3 to leave the x alone) $3x -4 \lt 2$ $3x \lt 6$ (add 4 to each side) $x \lt 2$ (divide each side by 3) so: $\frac{2}{3} \lt x \lt 2$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.