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# Which of the following inequalities is equivalent to −4 < x < 8?

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Which of the following inequalities is equivalent to −4 < x < 8?  [#permalink]

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22 Aug 2016, 02:59
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Which of the following inequalities is equivalent to −4 < x < 8?

A. |x - 1| < 7
B. |x + 2| < 6
C. |x + 3| < 5
D. |x - 2| < 6
E. None of the above

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Re: Which of the following inequalities is equivalent to −4 < x < 8?  [#permalink]

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22 Aug 2016, 03:45
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We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0

Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format

-4+y < x+y < 8+y

Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2

Thus, -6< x-2 < 6 => |x-2| < 6.

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Re: Which of the following inequalities is equivalent to −4 < x < 8?  [#permalink]

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22 Aug 2016, 20:28
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Bunuel wrote:
Which of the following inequalities is equivalent to −4 < x < 8?

A. |x - 1| < 7
B. |x + 2| < 6
C. |x + 3| < 5
D. |x - 2| < 6
E. None of the above

Given −4 < x < 8,
Now try to get into the mod form,
subtract two from both sides of the equation, (graphically the line remains the same)

-4 -2 < x-2 < 8-2 => -6 < x-2 < 6 and this is same as | x-2 | < 6, which is D

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Re: Which of the following inequalities is equivalent to −4 < x < 8?  [#permalink]

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22 Aug 2016, 21:59
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Bunuel wrote:
Which of the following inequalities is equivalent to −4 < x < 8?

A. |x - 1| < 7
B. |x + 2| < 6
C. |x + 3| < 5
D. |x - 2| < 6
E. None of the above

|x - a| = b

x is a distance 'b' away from 'a' on either side on the number line.

-4 < x < 8
Mid point of -4 and 8 is 2. Both -4 and 8 are 6 away from 2.
So the absolute value form will be |x - 2| < 6

For more, check: http://www.veritasprep.com/blog/2011/01 ... edore-did/
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Which of the following inequalities is equivalent to −4 < x < 8?  [#permalink]

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30 Dec 2018, 11:41
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The inequality $$|x-a|<b$$ is equivalent to inequality $$a- b < x< a+b$$ in which a is average of a+b & a-b, and b is mid distance from $$a-b$$and $$a+b.$$

So $$a = {(a+b) + (a-b)}/2$$
$$b= {(a+b) - (a-b)}/2$$

Let's put these values in original equation.

$$a= (-4+8)/2 =2$$

$$b={8-(-4)}/2 = 6$$

$$|x-2|<6$$

Similar question to practice: https://gmatclub.com/forum/which-of-the ... 59334.html
Thanks to MathRevolution for detail explanation.
Which of the following inequalities is equivalent to −4 < x < 8?   [#permalink] 30 Dec 2018, 11:41
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