Question

Which point is part of the solution of the inequality y ≤ |x+2|-3A.(-1,-1)B.(1,0)C.(0,0)D.(0,1)

Answer 1

We are going to test all options to see which is true and false.

The one that is true will be the point that is part of the solution.

`\begin{gathered} A) \\ (-1,-1) \\ y\leq\lvert x+2\rvert-3 \\ -1\leq\lvert-1+2\rvert-3 \\ -1\leq\lvert1\rvert-3 \\ -1\leq1-3 \\ -1\leq-2 \\ \text{Not true, so the point (-1,-1) is not a part of the solution} \end{gathered}`

We will move to the next option and test:

`\begin{gathered} B) \\ (1,0) \\ y\leq\lvert x+2\rvert-3 \\ 0\leq\lvert1+2\rvert-3 \\ 0\leq\lvert3\rvert-3 \\ 0\leq3-3 \\ 0\leq0 \\ \text{The above solution is true, so it is a point that is part of the solution.} \\ \text{The correct answer is option B.} \end{gathered}`