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

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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 break it down into two cases based on the outer absolute value. This gives us two equations:

|x - 4| - 6 = 2

and

|x - 4| - 6 = -2

. Solving the first equation, we have

|x - 4| = 8

, leading to two subcases:

x - 4 = 8

(which gives

x = 12

) and

x - 4 = -8

(which gives

x = -4

). For the second equation, [m]|x -…

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Comments

DhairyaJan 21, 2025

Thank you very much!

micheleMay 18, 2024

Good question

ElouanApr 29, 2024

Good question

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.