Solve 10 minus the absolute value of x plus 2 equals 12?

Answer 1

This could actually be 2 equations. I'll attempt to solve both.

10 - | x+2 | = 12

subtract 10 from both sides:

- | x+2 | = 2

multiply both sides by (-1):

| x+2 | = -2

this can't be solved.

Now for the second possibility based on the question:

10 - |x| + 2 = 12

combining constants on the lhs:

12 - |x| = 12

subtract 12 from both sides:

-|x| = 0

multiply both sides by (-1):

|x| = 0

the only way the absolute value of x could be 0 is if x = 0.

QED.