work your abs

[trided]

hi!
I have a question regarding this one

What is the value of y?

(1) 3|x2 - 4| = y - 2

(2) |3 - y| = 11

I met this kind of questions before and thought the solution could be like this one
l3-yl=11
y=-8 or y = 14
MGMAT learned me that in order to solve this one you should just try each number in the initial equation:
3 - -8= 11 OK
3-14=11 not ok

so B
but the correct answer here is C

what do I miss?

thanks!!!!

[RonPurewal]

I met this kind of questions before and thought the solution could be like this one
l3-yl=11
y=-8 or y = 14
MGMAT learned me that in order to solve this one you should just try each number in the initial equation:
3 - -8= 11 OK
3-14=11 not ok

hi -

yes, you should try these solutions in the original equation. (if the right side is just a NUMBER, as it is here, then you technically don't have to. however, if you don't know EXACTLY when you should and shouldn't check, then you should always check, just to be sure.)

the ORIGINAL equation contains an absolute value. do not neglect this.
i.e., you appear to be testing the equation
3 - y = 11
when the original equation is in fact
|3 - y| = 11

if we plug into the true original equation, -8 gives |11| = 11, and 14 gives |-11| = 11. both are true.

[imanemekouar]

Hi ron, I have a big question for you.When should a check the result that from an absolute value equation in this equation?And if I did What 's the conclusion?

[RonPurewal]

Hi ron, I have a big question for you.When should a check the result that from an absolute value equation in this equation?

it's not really worth memorizing complex rules as to when to check and when not to check.
instead, just check the solutions ANY time you have an absolute value equation.

it only takes a few seconds to plug into an equation and check, so, even if you are checking when you don't have to, it's no big loss.

And if I did What 's the conclusion?

if you plug the number in and it works, it's a solution.

if you plug a number in and it doesn't work, it's not a solution.

[harishamid]

Ron,

I thought we get two equations from Statement 1.

3|x^2 - 4| = y - 2
=> x^2 - 4 = (y - 2)/3 and -(x^2 - 4) = (y - 2)/3

solving these two equations

=> y = 2.

What I'm doing wrong in this?

Thanks

[harishamid]

Sorry my mistake. I know what I did wrong.

[mschwrtz]

Cool. Easiest post I've had to answer today.