SOLUTION: Which solution set satisfies the absolute value function:|x-3|- 5 ≤ 2? Answer Choices: a.)x ≤ 10 b.)-4 ≤ x ≤ 10 c.) x ≤ -4 or x ≥ 10 d.)

Instead of doing your problem for you, I'll do one EXACTLY IN EVERY
DETAIL like yours.  Then you can use it as a model to solve yours by.

|x-2| - 7 ≤ 3

Add 7 to both sides

|x-2| ≤ 10

±(x-2) ≤ 10

Make two inequalities by using +(x-4) in one and -(x-4) in the other

+(x-2) ≤ 10        -(x-2) ≤ 10
   x-2 ≤ 10          -x+2 ≤ 10
     x ≤ 12           -x ≤ 8 
                       x ≥ -8    (reversing because we divided by a negative)

x ≤ 12 says we shade left of 12 and x ≥ -8 says we shade right
of -8.   So we do both, darkening the endpoints because the inequalities
are ≤ and ≥, rather than < and >. 

--------●===========================================================●------
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14

That says we put -8 on the left, then ≤ x to stand for all the shaded 
part of the number line and a ≤ 12 on the right 

Answer:   -8 ≤ x ≤ 12

Now do yours EXACLY the same way.

Edwin