Equations with absolute values - MGMAT - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Equations with absolute values - MGMAT

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Sun Aug 17, 2008 1:44 pm

|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.

https://second-lap.blocked/

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Source: Beat The GMAT — Problem Solving | Sun Aug 17, 2008 1:44 pm

bourne159: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Tue Mar 11, 2008 6:30 am; Thanked: 6 times

by bourne159 » Sun Aug 17, 2008 2:00 pm

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?

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Sun Aug 17, 2008 3:17 pm

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

Thanks.

https://second-lap.blocked/

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