SOLUTION: How do i graph this absolute two variable inequality? y-3<|3x+15|+2

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Question 936299: How do i graph this absolute two variable inequality? y-3<|3x+15|+2
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for y in terms of x, and use the separate inequalities and their related lines.

y%3C3%28abs%28x%2B5%29%29%2B2%2B3
y%3C3%2Aabs%28x%2B5%29%2B5
Critical value is x=-5.


x%2B5%3E0
-
y%3C3%28x%2B5%29%2B5
y%3C3x%2B15%2B5
y%3C3x%2B20


x%2B5%3C0
-
y%3C3%28-x-5%29%2B5
y%3C-3x-15%2B5
y%3C-3x-10

What happens AT x=-5?
y%3Cabs%283%28-5%29%2B15%29%2B5%3F
y%3Cabs%28-15%2B15%29%2B5
y%3C5


SUMMARY
y%3C3x%2B20_________x%3E-5
y%3C-3x-10________x%3C-5

The equality would be:
graph%28300%2C300%2C-10%2C3%2C-3%2C10%2Cy=3%2Aabs%28x%2B5%29%2B5%29

The inequality is, keeping all graph regions in the same positions,
graph%28300%2C300%2C-10%2C3%2C-3%2C10%2Cy-3%3Cabs%283x%2B15%29%2B2%29