SOLUTION: solve the inequality 6+3y<4(3-x) for y and graph the solution. Please show me this step by step because I think I went wrong somewhere down the line, and I need to see where. Thank

Algebra ->  Graphs -> SOLUTION: solve the inequality 6+3y<4(3-x) for y and graph the solution. Please show me this step by step because I think I went wrong somewhere down the line, and I need to see where. Thank      Log On


   

Question 148204: solve the inequality 6+3y<4(3-x) for y and graph the solution. Please show me this step by step because I think I went wrong somewhere down the line, and I need to see where. Thanks in advance!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6%2B3y%3C4%283-x%29 Start with the given inequality.


6%2B3y%3C12-4x Distribute.


3y%3C12-4x-6 Subtract 6 from both sides.


3y%3C-4x%2B6 Combine like terms on the right side.


y%3C%28-4x%2B6%29%2F%283%29 Divide both sides by 3 to isolate y.


y%3C%28-4x%29%2F%283%29%2B%286%29%2F%283%29 Break up the fraction.


y%3C-%284%2F3%29x%2B2 Reduce

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Answer:

So the answer is y%3C-%284%2F3%29x%2B2



Now let's graph the equation y=-%284%2F3%29x%2B2 (replace the inequality sign with an equals sign)


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%29+ Graph of y=-%284%2F3%29x%2B2


Now plug in a test point (0,0) into the inequality y%3C-%284%2F3%29x%2B2


y%3C-%284%2F3%29x%2B2 Start with the given inequality.


0%3C-%284%2F3%29%2A%280%29%2B2 Plug in x=0 and y=0


0%3C2 Evaluate and simplify.


Since the inequality is true, this means that we shade the entire region that contains the point (0,0)


In other words, we simply shade the entire region that is below the line.


Graph of y%3C-%284%2F3%29x%2B2 with the shaded region in green



note: the boundary should be a dotted line.