If $|x - y| = |y - z| = 3$ and $x < y < z$ , what is the value of $|x - z|$ ?

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Official Explanation

Official

Given that

x < y

, we can deduce that

|x-y| = -(x-y) = 3

, which simplifies to

y-x = 3

. Similarly, since

y < z

is given, we can deduce that…

Comments

AntheaJan 17, 2024

how much time should this take to solve?

PrashantJun 11, 2024

Good question

What this question tests

Your ability to solve absolute-value equations and inequalities by considering both cases.

Dropping the absolute value bars entirely or missing that |x| = k has two solutions when k > 0.