SOLUTION: graph the inequality: 6x=4y<24

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Question 90138This question is from textbook
: graph the inequality: 6x=4y<24This question is from textbook

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph 6x%2B4y%3C24, we need to graph the equation 6x%2B4y=24 (just replace the inequality sign with an equal sign).
So lets graph the line 6x%2B4y=24 (note: if you need help with graphing, check out this solver)

+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+-%283%2F2%29x%2B6%29+ graph of 6x%2B4y=24
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality 6x%2B4y%3C24 with the test point

Substitute (0,0) into the inequality
6%280%29%2B4%280%29%3C24 Plug in x=0 and y=0
0%3C24 Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)
drawing%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-4%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-8%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-16%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-20%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-28%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-32%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-40%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-44%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-48%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-52%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%283%2F2%29x%2B6%2C-%283%2F2%29x%2B6%2B-56%29%29 Graph of 6x%2B4y%3C24 with the boundary (which is the line 6x%2B4y=24 in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)