AnkitK wrote:

what is x?

A.|x|<2

B.|x|=3x-2

You are missing an important point - let me explain.

We all know that if we have mods, we take two cases - positive and negative - and then solve the equation.

The point is - why do we do that?

If you remember, this is how we define mods

|x| = x if x is positive

and -x if x is negative

So basically, |x| takes different forms depending on whether x is positive or negative.

When I want to solve |x|=3x-2, I can't solve with |x|.

So I split it into two cases:

Case 1: x is positive

I get x = 3x - 2

x = 1

I accept this value of x since x has to be +ve and satisfy given equation. It does both.

Case 2: x is negative

-x = 3x - 2

x = 1/2

I reject this value since x should be negative for the equation to look like this.

So x can only take 1 value i.e. x = 1.

Remember, when you split |x| into two cases, you have to check that the value you get lies in the region in which you are expecting it to lie.

_________________

Karishma

Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!