Answer
$x \lt 2$ or, $x \lt 3-1$
Work Step by Step
Consider the inequality $|x-1| \lt |x-3|$
This gives:
$(x-1)^2 \lt (x-3)^2$
$\implies x^2-2x+1 \lt x^2-6x+9$
This gives: $4x \lt 8$
or, $x \lt 2$
This can be re-arranged as: $x \lt 3-1$
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 91: 128
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