linear inequalities Which Side Do I Shade?

Question

Solve the following system of linear inequalities by graphing.
x – 2y > 4
x < 4
Which Side Should be Shaded?

Solve the following system of linear inequalities by graphing.
x + 2y < 3
2x – 3y < 6
Which Side Should Be Shaded?

Solve the following system of linear inequalities by graphing.
3x + 4y < 12
x + 3y < 6
x > 0
y > 0
Which Side Should Be Shaded?

Answer 1

x – 2y > 4 -->x-4 > 2y --> y > x/2 -2
x < 4
Shade everything that is to the left of the dashed line x=4 and above the dashed line y = x/2 - 2

x + 2y < 3 --> 2y > -x + 3 --> y > -x/2 +3/2
2x – 3y < 6 --> 3y > 2x-6 --> y > 2x/3 -2
Shade everything that is above BOTH the dashed lines shown above.

3x + 4y < 12 --> 4y <12-3x --> y < 3-3x/4
x + 3y < 6 --> 3y < -x+6 --> y < -x/3 +2
x > 0
y > 0
So shade everything that is to the right of the y-axis(but not on it), and everything that is above the x-axis(but not on it), and everything that is below the dashed line y=-3x/4 + 3 and below the dashed line y = -x/3 +2.

Answer 2

1)
x - 2y > 4
x < 4

Your first step would be to put the first inequality in the form *like*
y = mx + b, *except* for the fact that there's no equal sign there.

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

Now, we divide both sides by -2. Note that multiplying or dividing by a negative number flips the inequality sign, so

y < (1/2)x - 2

At this point, what you're going to do is graph the line
y = (1/2)x - 2. Graph this as a dotted line.

Now, to find out which side you shade, test the point (0,0), by putting in x = 0 and y = 0 for the inequality. If you get a true statement, shade that part of the line. If you get a false statement, shade the OTHER side.

For y < (1/2)x - 2, plug in x = 0, y = 0, and this will give us

0 < (1/2)(0) - 2
0 < -2, which is a false statement.
Shade the part of the line that does NOT contain the point (0,0).

Now that you've shaded some part of the line, now shade x < 4. This is easy; x = 4 is a vertical line, so make a dotted vertical line at x = 4, and shade everything to the left of it.

The intersection of the shades should be your solution set.

Answer 3

upon determining the graph of the inequality, assume it as an equality and substitute a coordinate in any of the region. Most common is to substitute P(0,0). If the equality becomes true, he shaded region is the part containing that point. If it's false, take the region that does not contain the point.