Question

How do you graph the inequality `4x-2y<-3`?

Answer 1

See below

Explanation:

`4x-2y<-3`

Subtract `4x` to both sides

`-2y<-4x-3`

Divide through by `-2` and change the direction of the inequality.

`y>2x+3/2`

Now consider the limiting case where: `y=2x+3/2`

This is the straight line with slope `2` and `y-`intercept of `+3/2`

Then the graphic representation of the inequality is the area of all points where `y` is greater than but not equal to values on this line. Shown as the shaded area below.

graph{4x-2y<-3 [-12.66, 12.65, -6.33, 6.33]}