Begin the solution of |5m + 2| + 5 = 8 by subtracting 5 from both sides:
|5m + 2| = 3
Divide all 3 terms by 5 to isolate m: |m + 2/5| = 3/5
Case 1: m + 2/5 is already positive. The absolute value operator has no bearing. We have m + 2/5 = 3/5, or m = 1/5.
Case 2: (m + 2/5) is negative. Then we have -(m + 2/5) = 3/5, or
-m - 2/5 = 3/5, or
-m = 1, or m=-1
The solution set is {-1, 1/5}. Check both results via substitution.
