What is the value of x?

Question

(1) (|x| + 9)(x - 9) = 0
(2) (|x| - 9)(x + 9) = 0

Bunuel · Accepted Answer

OFFICIAL SOLUTION:

What is the value of x?

(1) (|x| + 9)(x - 9) = 0. For the product of two multiples to equal 0, either one of them (or both) must be 0. But since |x| + 9 = nonnegative + positive = positive, then |x| + 9 cannot be 0, which means that x - 9 = 0, or x = 9. Sufficient.

(2) (|x| - 9)(x + 9) = 0. Either |x| - 9 = 0 or x + 9 = 0. Thus x can be 9 or -9. Not sufficient.

Answer: A.

NavenRk · Answer

From (1) (|x| + 9) is a positive value. +ve * (x-9) = 0. Hence x=9. SUFFICIENT

From (2) X= + or - 9 . INSUFFICIENT.

Hence IMO A

Bowtye · Answer

IMO A

stmt 1: the first parenthesis will always be a positive number >0, so we want to focus on the second parenthesis.
 solve for x-9= 0 you get x=9 suff.

stmt 2: because the absolute value is in the parenthesis containing the subtraction, x could either be 9 or -9. Insuff.

sanguine2016 · Answer

My attempt:: 
(1) (|x| + 9)(x - 9) = 0
This equation gives only one solution x=9.
as |x|+9 cannot be 0. (x-9) will be equal to 0.
=> x=9.
Sufficient.

(2) (|x| - 9)(x + 9) = 0 
here either (|x|-9) can be 0 or (x+9) can be 0.
=> Either |x| = 9 => x = 9 or -9. OR x = -9.
Hence, Insufficient.

So Answer is A.

chetan2u · Answer

statement 1 gives us two bracket : (|x|+9) and (x-9)
(|x|+9) has 9, which is positive and |x|, which is non negative. So (|x|+9) will always be positive. 
Thus x-9 =0...........so x=9.. 
Sufficient

statement 2 gives us two bracket : (|x|-9) and (x+9)
Now, (|x|-9)=0, when |x|=9.
So x can be 9 or -9.
Insufficient

ans A

blanchif · Answer

hello guys,

Can someone explain this problem, i do not understand anything on the bracket difference. I do understand that |X| cannot be equal to -9 as an absolute value is always positie. Can someone explain this point ?

Thank you

chetan2u · Answer

I have added some more details in the earlier post. Please go through and if you still have any query, please revert.

bumpbot · Answer

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What is the value of x?

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