Question

How do you graph the inequality `20 > 2x+2y`?

Answer 1

See a solution process below:

Explanation:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: `x = 0`

`20 > (2 * 0) + 2y`

`20 > 0 + 2y`

`20 > 2y`

`20/color(red)(2) = (2y)/color(red)(2)`

`10 = y` or `(0, 10)`

For: `y = 0`

`20 > 2x + (2 * 0)`

`20 > 2x + 0`

`20 > 2x`

`20/color(red)(2) = (2x)/color(red)(2)`

`10 = x` or `(10, 0)`

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-10)^2-0.25)((x-10)^2+y^2-0.25)(2x+2y-20)=0 [-30, 30, -15, 15]}

Now, we can shade the left side of the line. We need to also make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(2x+2y-20) < 0 [-30, 30, -15, 15]}