What is the solution of |X - 1| = 5x + 10

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