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absolute values...

by topspin360 » Sat Aug 04, 2012 2:33 pm
For the problem below, why isn't the answer A? for |x+10| = 2x + 8, don't we have 2 equations that provide two different answers, hence the answer isn't clear: x+10 = 2x + 8, x+10 = -2x - 8?

Thanks.

What is the value of integer x?

(1) 2x^2+9<9x

(2) |x+10|=2x+8

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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by machichi » Sat Aug 04, 2012 2:44 pm
1) 2x^2 - 9x + 9 < 0
factor: (2x-3)(x-3)
x intercepts are x=3/2 or 3

Therefore, only x=2 works.

2) Let's check.
a) x+10=2x+8 (x=2)

2+10=2*2+8
12=12 (Check!)

b) x+10 = -2x-8 (x= -6)

-6+10= -2(-6)-8
4 = 4 (check!)

Two answers, so doesn't work.

It does need to be A.
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by eagleeye » Sat Aug 04, 2012 3:05 pm
topspin360 wrote:For the problem below, why isn't the answer A? for |x+10| = 2x + 8, don't we have 2 equations that provide two different answers, hence the answer isn't clear: x+10 = 2x + 8, x+10 = -2x - 8?
topspin360:

Whenever you do anything with |x|, you need to develop the cases:

Case 1: x+10 >= 0 => x >=-10
then |x+10| = x+10
x+10 = 2x+8
=> x=2 (We always check this value with our assumption, Is 2 > -10). Hence 2 is valid.
Case 2: x+10 <=0 => x <=-10
Then |x+10| = -(x+10)

-(x+10) = 2x+8
-x - 10 = 2x+8
=> 3x = -18
=> x = -6. (-6 is not less than -10. Hence -6 is not valid).

Therefore x = 2.

D is correct.

Alternatively, you can just do the +/- thing. But after you are done, test the values with the original equation.

For x= 2, 2x+8 = 12 and |x+10| = 12. This works.
For x=-6, 2x+8 = -12 + 8 = -4. A negative number can't equal |x+10| (which equals +4 here).
Hence x=2 is the only value and statement is sufficient. :)
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by topspin360 » Sat Aug 04, 2012 8:25 pm
makes sense eagleeye. thanks guys.
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