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If x is a number between -5 and 15

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If x is a number between -5 and 15 [#permalink]

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New post 19 Sep 2017, 07:26
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If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0
[Reveal] Spoiler: OA
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If x is a number between -5 and 15 [#permalink]

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New post 19 Sep 2017, 07:37
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petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0


Given, \(-5<x<15\). Add -5 to both sides of the inequality

\(-5-5<x-5<15-5\) or \(-10<x-5<10\)

This can be written as \(|x-5|<10\)

Option C
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If x is a number between -5 and 15 [#permalink]

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New post 19 Sep 2017, 09:25
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petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0

We know: -5 < x < 15

To find the range expressed in an absolute value inequality (or equation) you can use a fairly easy method. If needed, sketch a number line.

1) Find the midpoint,* which is 5, exactly halfway between -5 and 15.

2) Think about "distance from" to set up the expression, LHS

|x| = the distance of x from 0 on the number line

Similarly, |x - 5| is the distance of x from 5, the midpoint. (The point from which distance is measured has "moved" from 0 to 5, the midpoint of THIS range.)

That's the LHS

3) RHS?

Now use 5, midpoint, and 10, distance, as the "distance from": -5 is a distance of 10 from 5, and 15 is a distance of 10 from 5

The x here is not inclusive.

The distance of x from 5 cannot be 10 (which would be |x - 5| = 10), but it can be anything up to 10, namely

|x - 5| < 10

ANSWER C

You can check. (In fact, because these numbers are very manageable, if you got really stuck, you could work from the answer choices.)

|x - 5| < 10, remove absolute value bars, check the two cases

Case 1:
x - 5 < 10
x < 15

Case 2:
x - 5 > -10
x > -5

Together: -5 < x < 15 - Correct

ANSWER C

*Midpoint
\(\frac{(-5 + 15)}{2}\) = 5
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Re: If x is a number between -5 and 15 [#permalink]

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New post 21 Sep 2017, 16:25
petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0



It is important to note that, unless mentioned in the prompt, one needs to assume that the endpoints (-5 and 15) are not inclusive. As in, -5<x<15 and NOT \(-5\leq{x}\leq{15}\)
Re: If x is a number between -5 and 15   [#permalink] 21 Sep 2017, 16:25
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