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Inequalities (Number Line)

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by rahul.s » Sat Jan 09, 2010 5:35 am
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

On the number line, the shaded interval is the graph of which of the following inequalities? (The shaded region is from -8 to 4)

A. |x| <= 4
B. |x| <= 8
C. |x - 2| <= 4
D. |x - 2| <= 6
E. |x + 2| <= 6

OA is E

I'm confused between B, D and E
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by sanju09 » Sat Jan 09, 2010 6:27 am
I am sorry rahul, but if you resend this question with the figure of number line put as attachment and the following choices rewritten, so as to let us know what this '' sign really stands for, then we can probably help you out.

B. |x| <= 8
C. |x - 2| <= 4
D. |x - 2| <= 6
E. |x + 2| <= 6

Anyways, if the shaded part is from -8 to 4, then x ≥ -8 and x ≤ 4, in short -8 ≤ x ≤ 4. If I rewrite your choice E as |x + 2| ≤ 6, it means either x + 2 ≤ 6 or x + 2 ≥ -6, which results in either x ≤ 4 or x ≥ -8, or -8 ≤ x ≤ 4. Hence E could be correct in case my corrections match yours.

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by rahul.s » Sat Jan 09, 2010 7:58 am
Hi Sanju,

Thank you for your reply. I have attached the document containing the figure.
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by rahul.s » Sat Jan 09, 2010 8:01 am
What about option B and option D?

B says |x| <= 8, which is true.

Similarly, D says |x - 2| <=4, which is true as well.
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by papgust » Sat Jan 09, 2010 8:37 am
Hi,

B here is nothing but -8 <= x <= 8 which is not the shaded portion as it includes 5 to 8 as well.

D is nothing but -2 <= x <= 6 which is not the shaded portion.

But, E is |x+2| <= 6

-6 <= x+2 <= 6
-6-2 <= x <= 6-2
-8 <= x <= 4. Yes, this is the shaded portion.

So, E is right.
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