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Director
Joined: 28 Dec 2005
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Inequality and absolute values [#permalink]
 25 Jun 2006, 17:08
This is possibly a repost.....but if possible could someone explain the right way to solve this?
| 3x - 2 | <= | 2x - 5 |
The way I see it, we would end up with 4 possible equations:
3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)
Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment...
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Director
Joined: 16 Aug 2005
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Re: Inequality and absolute values [#permalink]
25 Jun 2006, 17:20
Futuristic wrote: This is possibly a repost.....but if possible could someone explain the right way to solve this?
| 3x - 2 | <= | 2x - 5 |
The way I see it, we would end up with 4 possible equations:
3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)
Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment...
Since you have to consider 4 different scenarios for absolute value problems like this one above, squaring it and then solving is faster.
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Director
Joined: 28 Dec 2005
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Re: Inequality and absolute values [#permalink]
25 Jun 2006, 17:47
gmatmba wrote: Futuristic wrote: This is possibly a repost.....but if possible could someone explain the right way to solve this?
| 3x - 2 | <= | 2x - 5 |
The way I see it, we would end up with 4 possible equations:
3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)
Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment... Since you have to consider 4 different scenarios for absolute value problems like this one above, squaring it and then solving is faster.
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Senior Manager
Joined: 09 Mar 2006
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Re: Inequality and absolute values [#permalink]
25 Jun 2006, 22:11
Futuristic wrote: gmatmba wrote: Futuristic wrote: This is possibly a repost.....but if possible could someone explain the right way to solve this?
| 3x - 2 | <= | 2x - 5 |
The way I see it, we would end up with 4 possible equations:
3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)
Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment... Since you have to consider 4 different scenarios for absolute value problems like this one above, squaring it and then solving is faster. If you square absolute values, the final equation will have exactly the same roots as the original. However if some of the variables are not in absolute values, you can end up with more roots then the original (consider |x|=2x+1 ). But you will never lose a root because of squaring.
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Director
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Great, thanks for confirming.
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