Question

Identify and fully explain the solution set to the absolute value equation below.|x| = -1

Answer 1

The given equation is:

$|x|=-1$

We need to start removing the absolute value term from the left. This creates a +- on the right side, so:

$x=\pm(-1)$

This leads us to two possible solutions:x

$\begin{gathered} x=+(-1)=-1 \\ x=-(-1)=1 \end{gathered}$

The solution set is x=-1,1.

Now, let's exclude the solutions that do not make |x|=-1, so:

$\begin{gathered} |-1|=1\ne-1 \\ |1|=1\ne-1 \end{gathered}$

As any of the solutions are true, then there is no solution.