Answer
This statement is false.
Work Step by Step
When y is negative, the two expressions are not equivalent.
For example, consider x=4 and y=-2
$|x-y|\overset?=|x|-|y|$
$|4-(-2)|\overset?=|4|-|-2|$
$|4+2|\overset?=4-2$
$6\ne2$
Algebra 1
by Hall, Prentice
Published by
Prentice Hall
ISBN 10:
0133500403
ISBN 13:
978-0-13350-040-0
Chapter 1 - Foundations for Algebra - 1-5 Adding and Subtracting Real Numbers - Practice and Problem-Solving Exercises - Page 36: 64
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