Equations with absolute values - MGMAT

[AleksandrM]

|x - 9/2| = 5/2

For the above equation, I calculated:

For x < 0

-x + 9/2 = 5/2

x = 2 [not true, because x is less than 0]

For x > 0

x - 9/2 = 5/2

x = 7 [true, because x is greaterthan 0]

However, according to MGMAT, both are correct. I want to understand why I am incorrect.

Thanks.

[bourne159]

Can you post the entire question?

The equation is |X-9/2| = 5/2
When you solve this the two cases are X-9/2 > 0 and X-9/2 <0
You assumed X > 0 and X <0 which are not the right equations.
Both cases give you two solutions for X.

Is the question asking how many solutions exist for X?

[AleksandrM]

The question is irrelevant. Yes, the question does assume that there are two solutions. I am trying to understand WHY not WHETHER.

Thanks.