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# If x is a number between -5 and 15

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Intern
Joined: 16 Mar 2017
Posts: 13

Kudos [?]: 10 [0], given: 15

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

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19 Sep 2017, 08:26
3
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Difficulty:

15% (low)

Question Stats:

71% (00:55) correct 29% (00:40) wrong based on 139 sessions

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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

Kudos [?]: 10 [0], given: 15

Director
Joined: 25 Feb 2013
Posts: 558

Kudos [?]: 254 [1], given: 34

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
If x is a number between -5 and 15 [#permalink]

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19 Sep 2017, 08:37
1
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2
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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

Kudos [?]: 254 [1], given: 34

Director
Joined: 22 May 2016
Posts: 983

Kudos [?]: 341 [2], given: 592

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

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19 Sep 2017, 10:25
2
KUDOS
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

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

*Midpoint
$$\frac{(-5 + 15)}{2}$$ = 5

Kudos [?]: 341 [2], given: 592

Manager
Joined: 30 May 2012
Posts: 220

Kudos [?]: 82 [0], given: 151

Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: If x is a number between -5 and 15 [#permalink]

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21 Sep 2017, 17:25
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 $$-5\leq{x}\leq{15}$$

Kudos [?]: 82 [0], given: 151

Re: If x is a number between -5 and 15   [#permalink] 21 Sep 2017, 17:25
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