When we have to solve a linear inequlity all we have to do is graph the line like we do for a normal linear equation,

For example :

y > 4x - 2

We just graph the line, like we normally would (we use a dotted line since the sign is > not >=). Then we would shade in the arae above the line since y is greater then that y value on the line.

---

y <= -2x - 3

For this one we graph the line with a solid line, since y may be equal to the y value at that point on the line. We then shade the area below the line (all values of y less than the value on the line).

---

4x + 4y > 8

We first have to solve for y.
y > -1x + 2.

Then graph the area above that line. To test to see if it works pick a point in the shaded area. Let's try (5,5). Does it work?

5 > -1(5) + 2

Yes, it works. So we have shaded the right area.

---

The only tricky thing with solving these equations is that we have to flip the sign of the inequality if we multiply or divide by a negative number, when we are solving the equation.

For example : -2y - 2x > 4
-2y > 2x + 4
y < -1x - 2

Notice : we had to flip the sign when we divided by the -2.

Graph the area under the line. Check a point in the shaded area, say point (-5,-5). It works in both our original equation and our new one, so we have shaded the correct side.

---

Look at : -1x > 5
we can see that only negative numbers would work to solve this inequality.

If we divide by -1 we get x > -5 and we see that our solution set is now wrong.

Flipping the sign we get x < -5 and our solution set is now correct.

---

Look at -1/2x >= 4
We can see that our solution set has to be a negative number. Multiplying both sides by -2 gives us :

x >= -8 which doesn't give us the correct result.
Flipping the sign gives us : x <= 8 which gives us the correct result.