Question

given the inequality 6x - 10y ≥ 9, select all possible solutionsA. (-1, 1)B. (-3, 4)C. (2, 1)D. (4, -2)E. (2, 8)F. (5, 2)

Answer 1

`6x-10y\ge9`

we simplify the expression to work easier

`\begin{gathered} 6x\ge9+10y \\ 6x-9\ge10y \\ (6x-9)/(10)\ge y \end{gathered}`

now we check each point replacing the coordinates and checking the inequality

A.

`\begin{gathered} (6(-1)-9)/(10)\ge(1) \\ \\ (-6-9)/(10)\ge1 \\ \\ -(15)/(10)\ge1 \\ \\ -1.5\ge1 \end{gathered}`

A is wrong because -1.5 isnt greater than 1 , so the inequality is wrong

B.

`\begin{gathered} (6(-3)-9)/(10)\ge(4) \\ \\ (-18-9)/(10)\ge4 \\ \\ (-27)/(10)\ge4 \\ \\ -2.7\ge4 \end{gathered}`

B is wrong because -2.7 isnt greater than 4

C.

`\begin{gathered} (6(2)-9)/(10)\ge(1) \\ \\ (12-9)/(10)\ge1 \\ \\ (3)/(10)\ge1 \\ \\ 0.3\ge1 \end{gathered}`

C is wrong because 0.3 isnt greater than 1

D.

`\begin{gathered} (6(4)-9)/(10)\ge(-2) \\ \\ (24-9)/(10)\ge-2 \\ \\ (15)/(10)\ge-2 \\ \\ 1.5\ge-2 \end{gathered}`

D is right because 1.5 is grreater than -2

E.

`\begin{gathered} (6(2)-9)/(10)\ge(8) \\ \\ (12-9)/(10)\ge8 \\ \\ (3)/(10)\ge8 \\ \\ 0.3\ge8 \end{gathered}`

E is wrong because 0.3 isnt greater than 8

F.

`\begin{gathered} (6(5)-9)/(10)\ge(2) \\ \\ (30-9)/(10)\ge2 \\ \\ (21)/(10)\ge2 \\ \\ 2.1\ge2 \end{gathered}`

F is Right because 2.1 is greater than 2