The given equation is:
[tex]|x|=-1[/tex]We need to start removing the absolute value term from the left. This creates a +- on the right side, so:
[tex]x=\pm(-1)[/tex]This leads us to two possible solutions:x
[tex]\begin{gathered} x=+(-1)=-1 \\ x=-(-1)=1 \end{gathered}[/tex]The solution set is x=-1,1.
Now, let's exclude the solutions that do not make |x|=-1, so:
[tex]\begin{gathered} |-1|=1\ne-1 \\ |1|=1\ne-1 \end{gathered}[/tex]As any of the solutions are true, then there is no solution.
