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On the number line, the shaded interval is the graph of which of the

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On the number line, the shaded interval is the graph of which of the  [#permalink]

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New post Updated on: 01 Aug 2018, 05:38
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On the number line, the shaded interval is the graph of which of the following inequalities?

A) \(|x| \leq 4\)

B) \(|x| \leq 8\)

C) \(|x - 2| \leq 4\)

D) \(|x - 2| \leq 6\)

E) \(|x + 2| \leq 6\)

Since the question appears in the Official Guide, I can see the GMAC's solution.

However, I barely have any knowledge about graphing inequalities. I know when to fill in and when not to fill in the dot and can graph a very easy inequality like x < 4, but this question is by far too much for me. For example, the solution says something about the midpoint of the interval from -8 to 4. Of course I can calculate the midpoint of that, but why is this the interval? And how do you go on with the calculation? I have never covered this at school.

Could someone please write a short guide about how to solve graphing inequalities problems? What one has to do and how you do it. I cannot find anything like that on the internet :(

Thanks a lot for any answer!

Originally posted by Flexxice on 03 Apr 2016, 22:12.
Last edited by carcass on 01 Aug 2018, 05:38, edited 2 times in total.
Edited the entire question
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Re: On the number line, the shaded interval is the graph of which of the  [#permalink]

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New post 04 Apr 2016, 02:31
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1
1
Flexxice wrote:
Attachment:
Math question.jpg

On the number line, the shaded interval is the graph of which of the following inequalities?

A) |x| <= 4

B) |x| <= 8

C) |x - 2| <= 4

D) |x - 2| <= 6

E) |x + 2| <= 6

Since the question appears in the Official Guide, I can see the GMAC's solution.

However, I barely have any knowledge about graphing inequalities. I know when to fill in and when not to fill in the dot and can graph a very easy inequality like x < 4, but this question is by far too much for me. For example, the solution says something about the midpoint of the interval from -8 to 4. Of course I can calculate the midpoint of that, but why is this the interval? And how do you go on with the calculation? I have never covered this at school.

Could someone please write a short guide about how to solve graphing inequalities problems? What one has to do and how you do it. I cannot find anything like that on the internet :(

Thanks a lot for any answer!


The absolute value function will be symmetrical about the centre. The centre point of the shaded region is -2. The distance on either side is 6. So the inequality will be
|x + 2| <= 6

If you plot this on the number line, you will shade 6 points to the right of -2 and 6 to the left of -2 (which is equal to the actual shaded region)

For more on this, check: http://www.veritasprep.com/blog/2011/01 ... edore-did/
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Re: On the number line, the shaded interval is the graph of which of the  [#permalink]

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New post 04 Apr 2016, 00:41
7
The Shaded region in the graph is -8 <= x <=4
Now we need to solve all the option choices to see which one is having this solution

A) |x| <= 4 means that -4 <= x <= 4 Not the answer we are looking for
B) |x| <= 8 means that -8 <= x <= 8 Not the answer we are looking for
C) |x-2| <= 4 means that -4 <= x-2 <= 4, which means -2 <= x <=6 Not the one
D) |x-2| <= 6 means that -6 <= x-2 <= 6, which means -4 <= x <=8 Not the one
E) |x+2| <= 6 means that -6 <= x+2 <= 6, which means -8 <= x <=4 This is what we were looking for.
Sp, Answer will be E

Hope it helps!

Flexxice wrote:
Attachment:
Math question.jpg

On the number line, the shaded interval is the graph of which of the following inequalities?

A) |x| <= 4

B) |x| <= 8

C) |x - 2| <= 4

D) |x - 2| <= 6

E) |x + 2| <= 6

Since the question appears in the Official Guide, I can see the GMAC's solution.

However, I barely have any knowledge about graphing inequalities. I know when to fill in and when not to fill in the dot and can graph a very easy inequality like x < 4, but this question is by far too much for me. For example, the solution says something about the midpoint of the interval from -8 to 4. Of course I can calculate the midpoint of that, but why is this the interval? And how do you go on with the calculation? I have never covered this at school.

Could someone please write a short guide about how to solve graphing inequalities problems? What one has to do and how you do it. I cannot find anything like that on the internet :(

Thanks a lot for any answer!

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Re: On the number line, the shaded interval is the graph of which of the  [#permalink]

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New post 04 Apr 2016, 06:50
Flexxice wrote:
Attachment:
Math question.jpg

On the number line, the shaded interval is the graph of which of the following inequalities?

A) |x| <= 4

B) |x| <= 8

C) |x - 2| <= 4

D) |x - 2| <= 6

E) |x + 2| <= 6

Since the question appears in the Official Guide, I can see the GMAC's solution.

However, I barely have any knowledge about graphing inequalities. I know when to fill in and when not to fill in the dot and can graph a very easy inequality like x < 4, but this question is by far too much for me. For example, the solution says something about the midpoint of the interval from -8 to 4. Of course I can calculate the midpoint of that, but why is this the interval? And how do you go on with the calculation? I have never covered this at school.

Could someone please write a short guide about how to solve graphing inequalities problems? What one has to do and how you do it. I cannot find anything like that on the internet :(

Thanks a lot for any answer!


Hi,
you can easily discard A, B and C as the total in each choice can never be 8 or 4, which are the edge points of the LINE...
For choosing between D and E, let me tell you what does a linear equality actually mean..
1) |x|<=4
this is SAME as |x-0|<=4..
this means x is less than or equal to 4 units away from 0 on either side.. so edge points are 0+4 on ONE end and 0-4 on the OTHER end...

2) |x - 1|<=4
this means x is less than or equal to 4 units away from 1 on either side.. so edge points are 1+4=5 on ONE end and 1-4=-3 on the OTHER end

similarly try for D and E, and you will realize E is the answer
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: On the number line, the shaded interval is the graph of which of the  [#permalink]

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New post 06 Apr 2016, 22:21
Thanks a lot to all of you! You guys really helped me a lot!

One last question:

If it asked about graphing /x + 2/ => 6, what would the illustration look like?
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Re: On the number line, the shaded interval is the graph of which of the  [#permalink]

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New post 06 Apr 2016, 23:16
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Flexxice wrote:
Thanks a lot to all of you! You guys really helped me a lot!

One last question:

If it asked about graphing /x + 2/ => 6, what would the illustration look like?


The shading would be the reverse of current shading in that case. Whatever is shaded now would be unshaded and whatever is not shaded right now, would be shaded.
In that case, the shaded region would be 4 and to the right of 4 and -8 and to the left of -8. All these values will satisfy |x+2| >= 6
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Re: On the number line, the shaded interval is the graph of which of the  [#permalink]

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New post 11 Apr 2017, 20:16
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Hi All,

You can use the answer choices 'against' the prompt to quickly eliminate options and zero-in on the correct answer.

From the given Number Line, we know that every number form -8 to +4 (inclusive) must 'fit' the correct answer, so we can start by plugging -8 and +4 into each of the choices. If you find an answer is not mathematically correct, then you can eliminate it. By plugging in these two values, we can quickly eliminate Answers A, C and D.

From here, we have to 'nitpick' what each inequality actually refers to in a bit more detail. Answer B tells us that |X| <= 8, but that Number Line would include X=5, X=6, X=7 and X=8 among it's solutions.... and the Number Line we were given does NOT. Thus, we can eliminate Answer B.

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