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

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: $x = 0$

$20 > \left(2 \cdot 0\right) + 2 y$

$20 > 0 + 2 y$

$20 > 2 y$

$\frac{20}{\textcolor{red}{2}} = \frac{2 y}{\textcolor{red}{2}}$

$10 = y$ or $\left(0 , 10\right)$

For: $y = 0$

$20 > 2 x + \left(2 \cdot 0\right)$

$20 > 2 x + 0$

$20 > 2 x$

$\frac{20}{\textcolor{red}{2}} = \frac{2 x}{\textcolor{red}{2}}$

$10 = x$ or $\left(10 , 0\right)$

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]}