Question

Which of the following is a solution of y> Ixl - 5? (-4,1) (-1,-4) (4,-1)

Answer 1

Given, the inequality y> Ixl - 5.

Consider the first option (x,y)=(-4,1).

Put x=-4 and y=1 in y> Ixl - 5 and check if it satifies the inequality.

`\begin{gathered} 1>\lvert-4\rvert-5 \\ 1>4-5 \\ 1>-1 \end{gathered}`

Since 1>-1 is correct, (-4,1) is a solution to the inequality y> Ixl - 5.

Now, consider second option (-1,-4).

Put x=-1 and y=-4 in y> Ixl - 5.

`\begin{gathered} -4>\lvert-1\rvert-5 \\ -4>1-5 \\ -4>-4 \end{gathered}`

Since -4>-4 is incorrect, (-1,-4) is not a solution to the inequality y> Ixl - 5.

Now, consider third option (4,-1).

Put x=4 and y=-1 in y> Ixl - 5.

`\begin{gathered} -1>\lvert4\rvert-5 \\ -1>4-5 \\ -1>-1 \end{gathered}`

Since -1>-1 is incorrect, (4,-1) is not a solution to the inequality y> Ixl - 5.

Therefore, the solution to the inequality y> Ixl - 5 is (-4,1).