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22 - | y + 14 | = 20

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Manager
Joined: 26 Feb 2015
Posts: 110
22 - | y + 14 | = 20  [#permalink]

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28 Feb 2015, 08:56
When I try solving this. I get

- | y + 14 | = +- 2 which gives me y = 16 and y = 12, however, in the solution it says y = - 16 and y = -12

why is the "-" before the | sign just vanishing?

shouldnt it be -y + 14 = +-2?

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Joined: 02 Aug 2009
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Re: 22 - | y + 14 | = 20  [#permalink]

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28 Feb 2015, 09:07
erikvm wrote:
When I try solving this. I get

- | y + 14 | = +- 2 which gives me y = 16 and y = 12, however, in the solution it says y = - 16 and y = -12

why is the "-" before the | sign just vanishing?

shouldnt it be -y + 14 = +-2?

hi erikvm..
when u open the mod, you will have two cases..
1)y+14=+-2.. y=-12 or y=-16..
2)-y-14=+-2... y=-12 or y=-16..
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Re: 22 - | y + 14 | = 20  [#permalink]

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28 Feb 2015, 09:11
chetan2u wrote:
erikvm wrote:
When I try solving this. I get

- | y + 14 | = +- 2 which gives me y = 16 and y = 12, however, in the solution it says y = - 16 and y = -12

why is the "-" before the | sign just vanishing?

shouldnt it be -y + 14 = +-2?

hi erikvm..
when u open the mod, you will have two cases..
1)y+14=+-2.. y=-12 or y=-16..
2)-y-14=+-2... y=-12 or y=-16..

ah so i either change both signs or neither?
Math Expert
Joined: 02 Aug 2009
Posts: 8292
Re: 22 - | y + 14 | = 20  [#permalink]

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28 Feb 2015, 09:29
erikvm wrote:
chetan2u wrote:
erikvm wrote:
When I try solving this. I get

- | y + 14 | = +- 2 which gives me y = 16 and y = 12, however, in the solution it says y = - 16 and y = -12

why is the "-" before the | sign just vanishing?

shouldnt it be -y + 14 = +-2?

hi erikvm..
when u open the mod, you will have two cases..
1)y+14=+-2.. y=-12 or y=-16..
2)-y-14=+-2... y=-12 or y=-16..

ah so i either change both signs or neither?

yes you are right..
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Re: 22 - | y + 14 | = 20  [#permalink]

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28 Feb 2015, 09:32
so its simply not that - | y + 14 | = +- 2 --> -y - 14 = +-2 . This is the only explaination that makes sense. If I change both/no signs. I get four different solutions?

-y - 14 = -2
-y - 14 = 2

y + 14 = -2
y + 14 =2
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Re: 22 - | y + 14 | = 20  [#permalink]

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28 Feb 2015, 14:01
Hi erikvm,

When dealing with certain types of math rules (in this case, Absolute Values), it's important that you NOT make things more complex than they need to be.

In this question, I'm going to *blank out* the absolute value, so that you can look at the rest of the equation...

22 - (something) = 20

Looking at this, you KNOW the value that must go in that parentheses.....it MUST be 2....

Now, I'm going to put the absolute value back in it's place...

|Y + 14| = 2

Since it's an absolute value, there should be two "results" that will equal 2.....+2 and -2

Thus....
Y + 14 = 2

AND

Y + 14 = -2

The respective solutions are Y = -12 and Y = -16

GMAT assassins aren't born, they're made,
Rich
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Joined: 26 Feb 2015
Posts: 110
Re: 22 - | y + 14 | = 20  [#permalink]

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01 Mar 2015, 05:34
EMPOWERgmatRichC wrote:
Hi erikvm,

When dealing with certain types of math rules (in this case, Absolute Values), it's important that you NOT make things more complex than they need to be.

In this question, I'm going to *blank out* the absolute value, so that you can look at the rest of the equation...

22 - (something) = 20

Looking at this, you KNOW the value that must go in that parentheses.....it MUST be 2....

Now, I'm going to put the absolute value back in it's place...

|Y + 14| = 2

Since it's an absolute value, there should be two "results" that will equal 2.....+2 and -2

Thus....
Y + 14 = 2

AND

Y + 14 = -2

The respective solutions are Y = -12 and Y = -16

GMAT assassins aren't born, they're made,
Rich

Thanks, that makes alot of sense. Question though, can I add/subtract on both sides just like any other expression? If I move the absolute value to the other side of the equality sign, does the "+" in | y + 14 | not change sign?

22 - | y + 14 | = 20 ---> 22 - 20 = | y - 14 |? Is the sign within the absolute value bracket forever bound to that specific sign?
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Re: 22 - | y + 14 | = 20  [#permalink]

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01 Mar 2015, 14:38
1
Hi erikvm,

While you can "move" the inequality to the other side of the equation, any signs "inside" the inequality must stay the SAME.

In this question, we have...

22 - |Y + 14| = 20

We are subtracting the second 'term' from the first 'term' to get the third 'term.'

A simpler example would be:

A - B = C

Moving the second term to the other side gives us....

A = C + B

In this question, it gives us...

22 = 20 + |Y + 14|

You can then subtract 20 from both sides...

2 = |Y + 14|

And solve just as we did in the prior post.

GMAT assassins aren't born, they're made,
Rich

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: 22 - | y + 14 | = 20  [#permalink]

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29 Nov 2019, 09:25
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Re: 22 - | y + 14 | = 20   [#permalink] 29 Nov 2019, 09:25
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