Question

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

Answer 1

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 `<`

`2y<=-4-x`; that means `y<=-4/2-x/2=-2-x/2`

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

`y=-x/2-2` and plot it in the coordinate's plane

3.- finally, consider the symbol `<=`. If `y<=expresion`, then the region-solution falls of below the line. If the symbol is `>=` 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]}