Question

How did they get 7? Please show the process

Answer 1

What I did

Answer 2

Oh I see what you did there...
You switched the 15 to positive, no no no :O

The final result should be positive, not the intermediate step though.
|4-15| = |-11| = 11

Answer 3

You were trying to apply like a plus/minus type thing to the absolute value?
Is that what was going on?

Answer 4

Absolute value only takes on both signs if it has a variable contained inside.\[\large\rm |\color{orangered}{x}|=\pm \color{orangered}{x}\]A number however only takes on one of them,\[\large\rm |\color{orangered}{7}|=+\color{orangered}{7}\]So you can see that 7 takes on the positive,\[\large\rm |\color{orangered}{-5}|=-(\color{orangered}{-5})=5\]While -5 takes the negative.

Answer 5

Maybe that was a little too fancy :)
My point is simply that,\[\large\rm |-11|\ne \pm 11\]

Answer 6

Thank!