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 5The 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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