# How do you graph the inequality x + 2y< = -4?

Mar 29, 2018

See below.

#### Explanation:

The solution of this type of inequations is a plane region.

Allways proceed as follows.

1.- leave $y$ alone in one side of symbol $<$

$2 y \le - 4 - x$; that means $y \le - \frac{4}{2} - \frac{x}{2} = - 2 - \frac{x}{2}$

2.- Treat this last expresion as a normal function., It's say

$y = - \frac{x}{2} - 2$ and plot it in the coordinate's plane

3.- finally, consider the symbol $\le$. If $y \le \exp r e s i o n$, then the region-solution falls of below the line. If the symbol is $\ge$ the solution is above the line. If symbols include $=$ the line is part of solution, if not, then the line is not included in solution (mark it with a dotted line).

See the graph (The dark blue area is the solution)
graph{y<=-x/2-2 [-10, 10, -5, 5]}