How many solutions are there to the equation below? |x| = - 31

No solutions

Step-by-step explanation:

The absolute value always returns a positive value, thus cannot be equal to - 31

Break down the problem into these two equations;

x = - 31

-x = - 31

Solve for the 1st equation; x = - 31

x = - 31

Solve for the 2nd equation; - x = - 31

x = 31

Collect all solutions

x = ±31

Check the solution

When x = - 31, the original equation; |x| = - 31 does not hold true. Thus, we will drop x = - 31 from the solution set.

Check the solution again;

When x = 31, the original equation |x| = - 31 does not hold true as well. Thus we will drop x = 31 from the solution set.

Therefore,

No solution exists to this equation.