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There is no big flaws, but it is not fully mathematically correct. When opening the absolute value you should add constraints which you use. In other words, \(|x|=x\) if \(x>=0\)

So, the precise solution is as follows:

\(|x|=3x-2\)

\(x=3x-2 , x>=0\) \(-x=3x-2, x<0\)

\(2x=2, x>=0\) \(4x=2, x<0\)

\(x=1, x>=0\) \(x=0.5, x<0\)

So, the only answer is x=1. Good luck! Try to solve some more problems with absolute values (both equations and inequalities)
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If my post is useful for you not be ashamed to KUDO me! Let kudo each other!

Came across this rather interesting quant question, and thought of sharing it with folks here:

|x| = 3x - 2

a. 1 b. 1/2 c. 1 and 1/2 d. -1/2 e. -1

I know it's fun to solve when you know what you are doing (and more importantly, why you are doing it) and the graph method is especially satisfying but don't forget a very basic trick in such questions. When you have values for x in the options, and an equation in the question, we could just plug the values in. Since x = 1 satisfies the equation and x = 1/2 doesn't, answer has to be (A).
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I know it's fun to solve when you know what you are doing (and more importantly, why you are doing it) and the graph method is especially satisfying but don't forget a very basic trick in such questions. When you have values for x in the options, and an equation in the question, we could just plug the values in. Since x = 1 satisfies the equation and x = 1/2 doesn't, answer has to be (A).

Wow thanks, you are correct i had overlooked this option.. do you think such questions will come in the real gmat, where plugging the value may reveal the answer?

I know it's fun to solve when you know what you are doing (and more importantly, why you are doing it) and the graph method is especially satisfying but don't forget a very basic trick in such questions. When you have values for x in the options, and an equation in the question, we could just plug the values in. Since x = 1 satisfies the equation and x = 1/2 doesn't, answer has to be (A).

Wow thanks, you are correct i had overlooked this option.. do you think such questions will come in the real gmat, where plugging the value may reveal the answer?

Just another simple approach. Since |x| is always positive so 3x - 2 should always be positive for this equation to be true. You can simply rule out options (D) and (E), as any negative values of x will make 3x-2 negative. For 1/2, again 3x-2 becomes negative. So only option left is (A).

Wow thanks, you are correct i had overlooked this option.. do you think such questions will come in the real gmat, where plugging the value may reveal the answer?

Thanks.

Sure it is possible. That is why it is good to keep this in mind since a relatively tricky question can be easily solved this way. Though, GMAC is wise to such tricks and since these questions don't involve much work on your part, don't expect the options to help you often (nevertheless, you should always keep one eye on the options), at least not right in the beginning. If you do get such a question, it may not be a very high level question.
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