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Sagot :
Let's solve the equation:
[tex]\begin{gathered} \lvert x+2\rvert=0 \\ x+2=\pm0 \\ x=-2\pm0 \\ x=-2 \end{gathered}[/tex]Let's now solve the inequality:
[tex]\begin{gathered} \lvert x+2\rvert\ge0 \\ x+2\ge0\lor x+2\leq0 \\ x\ge-2\lor x\leq-2 \end{gathered}[/tex]Therefore the solution of the inequality is:
[tex](-\infty,-2\rbrack\cup\lbrack-2,\infty)[/tex]Once we know both solutions we conclude that:
The equation has one solution and the inequality have a range of solutions. Therefore the correct choice is the third option.
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