Solve the absolute value equation. |5m + 2| + 5 = 8

5m+7=8

5m=1

m=1/5

-5m-2+5=8

-5m+3=8

-5m=5

m=-1

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.