Graphing Compound Inequality?

Question

If possible could someone explain the steps to solve, and graph these compound inequalities??

x >/= -2y and
x - 3y < 6


AND...

3 - x < y + 2 or
x > y + 5

Thanks for the help! Test is Friday!!!!!!!!

Answer 1

Graphing inequalities is much like graphing lines. The only differences are (1) sometimes you use dashed lines to represent > or < (as opposed to >= or <=, which use solid lines), and (2) you're shading in a region that satisfies the inequality.

For the first set, graph the first inequality as if it were a line:

x = -2y
y = -x/2

Graphically, that's a line with a slope of -1/2 and passing through the origin. Since it's a >= inequality, use a solid line. And as for the shading, you need to shade the side of the line that works for the inequality. How do you know? Let's just pick a point and test it out. Say we use (500, 0) which is "above" the line. We would have:

x >= -2y
500 >= -2(0)
500 >= 0

Since this works out, we shade the "above" side of the line we just drew.

Graph the other inequality in the same way - graph the line first (in this case, you'd be using a dashed line since the inequality has a< sign), and then pick a point so you can figure out what side to shade in. The area that overlaps is the solution to your system of inequalities.

Answer 2

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