Solve the following system of linear inequalities by graphing.?

Question

x – 2y > 4
x < 4

which side is shaded?

Answer 1

x - 2y > 4
x < 4

The trick here is to put the first inequality in something *like* slope intercept form. Recall the form y = mx + b; we put the inequality in this form, with the difference being that this is an inequality and not equality.

x - 2y > 4
-2y > -x + 4

Now, divide both sides by (-2). This will flip the inequality.

y < (1/2)x - 2

What you do at this point is GRAPH y = (1/2)x - 2.
You're going to be shading one side of the line, and to know which side you're shading, plug in the value x = 0, y = 0.
If you get a true statement, shade the side of the line which includes (0,0). If you get a false statement, shade the side of the line that does NOT include (0,0).

y < (1/2)x - 2, and plugging in x = 0, y = 0,
0 < 0 - 2
0 < -2, which is false.

Shade the part of the line that does not encompass (0,0).

For the inequality x < 4, graph the (vertical) line x = 4, and then shade everything to the left of it.

One other important note:

When you have an inequality that is _strictly_ less than, or _strictly_ greater than (i.e. < or >), you have to created a *dotted* line, and then shade as normal.

If you have an inequality that is "less than or equal to" or "greater than or equal to", you create a solid line, and shade as normal.