Determine the median of all values of x that… | GMAT Sprint

Free Practice Question

PS · Problem Solving

605-655

Absolute Values/Modules

Determine the median of all values of x that fulfill the equation $||x - 4| - 6| = 2$ .

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Explanation

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Official Explanation

Official

To solve the equation

||x - 4| - 6| = 2

, we first set

y = |x - 4|

. This transforms our equation into

|y - 6| = 2

. This absolute value equation can be split into two cases:

y - 6 = 2

and

y - 6 = -2

. Solving these gives us

y = 8

and

y = 4

. Reverting back to x, we have two equations:

|x - 4| = 8

and

|x - 4| = 4

. From

|x - 4| = 8

, we find [m]x =…

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Comments

DharunMar 4, 2025

Thankss

VatadeOct 14, 2024

thanks

YuJun 5, 2024

thanksss

What this question tests

What it tests

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

Common trap

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

Determine the median of all values of x that fulfill the equation ∣∣x−4∣−6∣=2||x - 4| - 6| = 2∣∣x−4∣−6∣=2.