Question 178190: The problem is y less than x+3 and y greater then -x+2 I have to graph the compound inequality. This is my first time taking algebra but I know how to do some but not this.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I can't show you the graphs on this site because it won't render shaded half-planes, but I can tell you what to do.
Replace the inequality sign with an equal sign:
Now graph the equation (slope of 1, y-intercept 3), but since the original inequalty did not include equals, i.e., it was  rather than  , make the line a dashed line.
Next select any point that is not on the line. Any time the line does not pass through the origin, (0, 0) is an excellent choice. Substitute the coordinates of the selected point in the original inequality. If the result is a true statement, then shade in the half-plane containing the point. If the result is false, shade in the other half.
 , is true, so shade in the half-plane containing the origin.
Next, graph the other inequality on the same set of coordinate axes, following the same procedure outlined above. This second inequality doesn't contain 'or equal' either so this graph will also have a dashed line. Determining the side of the line to shade is done the same way, and the origin (0, 0) is a good choice for this one too.
The solution set for the system of inequalities is the area of the graph where the two shaded half-planes overlap. Points on the dashed lines are not included in the solution set.
The graphs below are the graphs of the two lines. Your picture should have these as dashed lines. Everything below and to the right of the red line should be shaded and everything above and to the right of the green line should be shaded. The overlap is the V-shaped area on the right.
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