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What is the solution of the equation |x - 2| + 2x = 4 - x?

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What is the solution of the equation |x - 2| + 2x = 4 - x?

by Max@Math Revolution » Fri Aug 07, 2020 12:09 am

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[GMAT math practice question]

What is the solution of the equation |x - 2| + 2x = 4 - x?

A. -2
B. -1
C. 0
D. 1
E. 2
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Re: What is the solution of the equation |x - 2| + 2x = 4 - x?

by Max@Math Revolution » Sun Aug 09, 2020 11:03 pm
=>

Case 1: x ≥ 2
|x - 2| + 2x = 4 - x
⇔ x – 2 + 2x = 4 – x
⇔ x + 2x + x = 4 + 2
⇔ 4x = 6
⇔ x = 3/2
However, 3/2 does not satisfy the assumption x ≥ 2.
Thus, we don’t have any solution under the assumption x ≥ 2.

Case 2: x < 2
|x - 2| + 2x = 4 - x
⇔ -(x - 2) + 2x = 4 – x
⇔ -x + 2 + 2x = 4 - x
⇔ -x + 2x + x = 4 - 2
⇔ 2x = 2
⇔ x = 1
Since 1 satisfies the assumption x < 2, 1 is taken as a solution for the equation.

Therefore, D is the correct answer.

Answer: D
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