Question

4x-2y<-2

a) (2,8) b) (0,1) c) (3,7) d) (5,8)​

Answer 1

a) (2, 8)

Explanation:

The easiest way is to insert the coordinates into the inequality.

a) (2, 8)

`\begin{array}{rcl}4(2) - 2(8) & < & -2\\8 - 16 & < & -2\\-8 &< & -2\\\end{array}\\\textbf{TRUE}`

b) (0, 1)

`\begin{array}{rcl}4(0) - 2(1) & < & -2\\0 - 2 & < & -2\\-2 &< & -2\\\end{array}\\\text{False}`

c) (3, 7)

`\begin{array}{rcl}4(3) - 2(7) & < & -2\\12 - 14 & < & -2\\-2 &< & -2\\\end{array}\\\text{False}`

d) (5, 8)

`\begin{array}{rcl}4(5) - 2(8) & < & -2\\20 - 16 & < & -2\\4 &< & -2\\\end{array}\\\text{False}`

You could also plot the inequality and test the points. You would get a graph like the one below. Point (2, 8) is the only one that satisfies the inequality. Points (0, 1) and (3, 7) do not satisfy the inequality because they are on a dashed line.