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Manhattan GMAT - Number Properties - Chapter 3 Practice Q5

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by selango » Mon Nov 15, 2010 7:59 pm
Only when x=4.

x-4=4-x

x-4=-(x-4)

2(x-4)=0

x=4


Hope this clarify!!
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by Brian@VeritasPrep » Tue Nov 16, 2010 9:29 am
Nice explanation, selango - I'll just add that the strategy here is really to set up an equation like you did:

"When is x - 4 equal to 4 -x"

Sets up as:

When does: x-4 = 4-x

Then you can do the same thing to both sides to keep the equation balanced (I'd steer clear of messing with negative multiplication and just add x to both sides and 4 to both sides to cancel out the negative numbers)

2x = 8
x = 4


A lot of times these word problems just come down to your ability to put the words into mathematical terms so that you can get to work on the algebra. Be careful when setting up equations, but once you have them hopefully you're comfortable enough with algebra that it's just a matter of finishing those steps.
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by umasastry » Tue Nov 16, 2010 10:49 am
Hi Selango and Brian,

Thanks for the application but I made a mistake while posting my question.
The actual question was
When is |x-4|=4-x...i missed the absolute value sign?

Could you please clarify this one.

thanks,
Uma
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by Rahul@gurome » Tue Nov 16, 2010 11:49 am
umasastry wrote: When is |x - 4| = 4 - x?
The absolute value gives rise to two cases:
  • (1) |x - 4| = (x - 4) if (x - 4) ≥ 0 => x ≥ 4
    ... In this case, |x - 4| = (4 - x) => (x - 4) = (4 - x) => 2x = 8 => x = 4
    (2) |x - 4| = (4 - x) if (x - 4) < 0 => x < 4
    ... In this case, |x - 4| = (4 - x) => (4 - x) = (4 - x) => Satisfies for any x < 4.
Thus combining these two, we get the given condition is possible for all x ≤ 4.
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