Break down the problem into these two equations;
x - 1 = 5x + 10
-(x - 1) = 5x + 10
Now solve the first equation; x - 1 = 5x + 10
x = -11/4
Solve the second equation; -(x - 1) = 5x + 10
x = -3/2
Collect all solutions
x = -11/4, -3/2
Check solution
So, when x = -11/4, the original equation |x - 1| = 5x + 10 doesn't hold true. We will drop x = -11/4 from the solution set.
Therefore,
x = -3/2
