Hi, it was 6 years since my last math course, and even then, it wasnt much since I am a political science major. In any case, as I am going through MGMAT guides (im on 3rd one now) I have a question on an example of an absolute value that MGMAT guide 3 (third edition).
The question is if |x-2|=|2x-3|, what are the possible values for x? There are two possibilities for x where the equations have the same signs and other is where one sign is negative. I have no problems when it is a same sign, nor do I have problems solving for x. What throws me off is when the negative value of the equation, which is equal to x=5/3 gets plugged in to check the answer. So the whole problem goes like that:
Case B.
(x-2)=-(2x-3) -----> 3x=5-----> x=5/3
Checking validity by plug in:
|5/3-2|=|2(5/3)-2| both sides equal 1/3 How can that be? Left hand side is ok because it is equal to |-1/3|. But when plugging in, how did they get -2 instead of -3 on the right side when original equations clearly states |2x-3|? I need that to be explained; and even so, wouldnt rest of it go like that: 2(5/3)=10/3 thus 10/3-2(1/3)= 8/3? or if there was -3 then equation would equal 7/3, and both sides are not equal to eachother?
The question is if |x-2|=|2x-3|, what are the possible values for x? There are two possibilities for x where the equations have the same signs and other is where one sign is negative. I have no problems when it is a same sign, nor do I have problems solving for x. What throws me off is when the negative value of the equation, which is equal to x=5/3 gets plugged in to check the answer. So the whole problem goes like that:
Case B.
(x-2)=-(2x-3) -----> 3x=5-----> x=5/3
Checking validity by plug in:
|5/3-2|=|2(5/3)-2| both sides equal 1/3 How can that be? Left hand side is ok because it is equal to |-1/3|. But when plugging in, how did they get -2 instead of -3 on the right side when original equations clearly states |2x-3|? I need that to be explained; and even so, wouldnt rest of it go like that: 2(5/3)=10/3 thus 10/3-2(1/3)= 8/3? or if there was -3 then equation would equal 7/3, and both sides are not equal to eachother?
