Question

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

Answer 1

No solutions

Explanation:

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

Answer 2

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.