Whatever is inside the absolute value sign becomes positive, regardless of whether it is negative or positive. For example, |-3| = 3, just as |3| = 3. (The absolute value of 0 is always 0.)
In your problem, the variable expression (5m + 1) could be either positive or negative, and still have an absolute value of 13. This means we have to try both possibilities.
We set it up this way, removing the absolute value sign and using two equations:
5m + 1 = 13 OR -(5m + 1) = 13
We solve each part separately:
5m + 1 = 13 OR -5m -1 = 13
-1 -1 +1 +1
______________ _____________
5m = 12 OR -5m = 14
m = 12/5 OR m = -14/5
You could also set it up this way, which is algebraically the same:
5m + 1 = 13 OR 5m + 1 = -13
- 1 -1 -1 -1
___________________ ______________
5m = 12 OR 5m = -14
m = 12/5 OR m = -14/5
