CAT Math Absolute Value Question

[loocrabsuks]

What is x?

(1) |x| < 2

(2) |x| = 3x - 2

Ans for this problem is B. I do not understand why when we get two values as the answer x = 2 and x = 1/2 (x<0) we eliminate x = 1/2. Can you please explain?

Thanks,

[dunhammn2004]

The answer X = -1/2 actually is not an answer. If you check the solution you get 1/2 = - 3/2 - 2 = -7/2 which is not true.

The other solution, x=1 makes sense so it is the one correct answer.

[RonPurewal]

What is x?

(1) |x| < 2

(2) |x| = 3x - 2

Ans for this problem is B. I do not understand why when we get two values as the answer x = 2 and x = 1/2 (x<0) we eliminate x = 1/2. Can you please explain?

Thanks,

when you solve
* absolute value equations
* radical equations

you have to CHECK your answers at the end of the problem, to make sure that they are not "fake answers"!

in this problem, splitting the equation gives x = 3x - 2 or x = -3x + 2.
solving the first gives x = 1. plugging back in, we see that this solution is valid.
solving the second gives x = 1/2. plugging back in, we see that this solution is not valid (it gives 1/2 = -1/2).

so, only x = 1.

[rico16rad]

What is x?

(1) |x| < 2

(2) |x| = 3x - 2

Ans for this problem is B. I do not understand why when we get two values as the answer x = 2 and x = 1/2 (x<0) we eliminate x = 1/2. Can you please explain?

Thanks,

when you solve
* absolute value equations
* radical equations

you have to CHECK your answers at the end of the problem, to make sure that they are not "fake answers"!

in this problem, splitting the equation gives x = 3x - 2 or

x = -3x + 2

.solving the first gives x = 1. plugging back in, we see that this solution is valid.
solving the second gives

x = 1/2.

plugging back in, we see that this solution is not valid (it gives 1/2 = -1/2).

so, only x = 1.

hi,
Please Let me know if i am wrong , What you said is
x=-3x+2 if i put x=1/2 doesn't satisfy the equation x=-3x+2
how is that possible ?Sir
x=-3(1/2)+2
x=(-3+4)/2= 1/2

am i wrong ..If i am wrong please let me know ..Thanks

[ganeshraj]

When x = 1, |x|=1 & 3x-2 =1 , therefore |x|=3x-2.
When x = 1/2, |x|=1/2 & 3x-2 =-1 /2 , therefore |x|!=3x-2.

[esledge]

Please Let me know if i am wrong , What you said is
x=-3x+2 if i put x=1/2 doesn't satisfy the equation x=-3x+2
how is that possible ?Sir
x=-3(1/2)+2
x=(-3+4)/2= 1/2

am i wrong ..If i am wrong please let me know ..Thanks

rico16rad, your mistake was plugging in to the "broken" (i.e. absolute values removed) equation to check. You always want to plug the solutions back into the original equation to see whether it checks out with the absolute value, as ganeshraj did.