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

1 Answer
Oct 8, 2017

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]}