Question

Determine if the ordered pair (6, 4) is a solution to the inequality y is greater than negative one half times x plus 7.

Answer 1

Let's write the inequality down:

`y > -(1)/(2)x+7`

Let's plug the values x=6, y=4:

`4 > -(1)/(2)\cdot 6+7 \iff 4 > -3+7 \iff 4>4`

Which is false, unless you meant "greater than or equal to". In that case, the pair is a solution.

Answer 2

No, the ordered pair(6,4) is not a solution to y > (-1/2)x + 7.

Explanation:

First lets establish the area of the solutions of y > (-1/2)x +7. Because it is y>, this means that the area of the solutions is anything above the y value not including the y value itself. So, if we plug in x=6 into the equation, we will get y=4, yet because it is not greater than the y-value itself(4>4 is not true), (6,4) is not a solution to the equation. If it was y is greater than or equal to, the story would be different and (6,4) would be a solution since it includes the y-value itself.