You begin by getting the absolute value equation on its own. You do that by adding 1 to both sides, then dividing by -8.
|-2x+1|= 5
Then you solve the absolute value equation by writing two equations. One equation is set to equal 5, while the other equation is set to equal -5.
-2x+1= 5
and
-2x+1= -5
Solve each like normal equations and you get x=-2 and x=3
