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Sagot :
Given:
The inequality is given as 5x + 2y > 6.
The objective is to select all the correct options satisfying the inequality.
Explanation:
Consider the point (x,y) = (0,5) and substitute in the given inequality.
[tex]\begin{gathered} 5(0)+2(5)>6 \\ 0+10>6 \\ 10>6 \end{gathered}[/tex]Thus, the point satisfies the inequality.
Consider the point (x,y) = (3,1) and substitute in the given inequality.
[tex]\begin{gathered} 5(3)+2(1)>6 \\ 15+2>6 \\ 17>6 \end{gathered}[/tex]Thus, the point satisfies the inequality.
Consider the point (x,y) = (3,-4) and substitute in the given inequality.
[tex]\begin{gathered} 5(3)+2(-4)>6 \\ 15-8>6 \\ 7>6 \end{gathered}[/tex]Thus, the point satisfies the inequality.
Now, consider the point (x,y) = (-4,1) and substitute in the given inequality.
[tex]\begin{gathered} 5(-4)+2(1)>6 \\ -20+2>6 \\ -18>6 \end{gathered}[/tex]Thus, the point does not satisfy the inequality.
Hence, options (1), (2), and (3) are the correct answer.
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