Which equation gives the values of all numbers seven units away from 4

gmatbusters posted the fastest and easiest way to solve, IMO. If you cannot recall the formulation, or get mixed up, a couple of details might help.

1) watch the SIGN inside the brackets
|x| = the distance OF x from 0
|x - 3| is the distance OF x FROM +3
We measure distance by subtracting. There's one hint:

A minus sign inside the brackets indicates distance of x from a POSITIVE number.

The distance of x from a negative number is written
x - (-3), which = (x + 3)

In this context, distance from a negative number will be indicated by a plus sign (+) inside the brackets.

Even if you're confused about where 7 and 43 go, both are positive. Whatever is INSIDE the brackets will be preceded by a minus sign.
Eliminate answers A and E

2) Take the problem at face value. It mentions the numbers 43 and 7, not 14. Ignore C for now

We're down to answers B and D. Solve them. Drawing a number line helps here, I think.

B. |x – 7| = 43
Case 1: x - 7 = 43
x = 50
Case 2: -(x - 7) = 43
-x + 7 = 43
-x = 36
x = -36

On this number line, boldface type = a discrete dot. There are two points, x = -36 and x = 50. Nothing in between is highlighted.

<--(-36)-------(0)---------------(50)-->

Prompt says "all numbers [that are] seven units away from 43." Write in 43 on the number line.

<--(-36)-----(0)--------(43)--(50)-->
Well, 50 is indeed 7 units away from 43.

But -36? No, -36 is many more than seven units away from 43. WRONG.
No need to calculate. It is obvious that -36 is more than seven units away from 43.
Then again, this can be a tough crowd... the distance of -36 from 43 is: 43 - (-36) = 79

Eliminate B

D. |x – 43| = 7
Case 1: x - 43 = 7
x = 50
Case 2, -(x - 43) = 7
-x + 43 = 7
-x = -36)
x = 36

At this point the logic might be clearer, such that you could investigate 36 and 50 in relation to 43. If not, draw a number line.

<--(0)------(36)----------------(50)-->

Back to the prompt: "all numbers that are seven units away from 43." Write in 43

<--(0)------(36)-----(43)------(50)-->

36 is seven units away from 43
50 is seven units away from 43
We have gone both directions on the number line.
There are no other numbers that are exactly 7 units away from 43. CORRECT

Answer D

For absolute value as distance, an exceptional introduction is mikemcgarry ,GMAT Math: Understanding Absolute Values

Other superb resources include but are not limited to chetan2u , Absolute Modulus, a Better Understanding
and Bunuel , Ultimate GMAT Quantitative Megathread: 10. Absolute Value