SOLUTION: Thanks for your help in advance.I can't seem to get these questions to make sense to me... Suppose {{{2x^2> 3x+2}}} -Find critical values of the related equation -Use a table

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Thanks for your help in advance.I can't seem to get these questions to make sense to me... Suppose {{{2x^2> 3x+2}}} -Find critical values of the related equation -Use a table       Log On


   

Question 1074755: Thanks for your help in advance.I can't seem to get these questions to make sense to me...
Suppose 2x%5E2%3E+3x%2B2
-Find critical values of the related equation
-Use a table of intervals, subdivided by the critical values, to test the inequality.
-Write the solution set using interval notation.
-Make a graph of the related equation to verify your solution.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-3x-2%3E0
%282x%2B1%29%28x-2%29%3E0
So the critical points (zeros) are:
2x%2B1=0
2x=-1
x=-1%2F2
and
x-2=0
x=2
Break up the number line using these critical values.
Region 1: (-infinity,-1%2F2)
Region 2: (-1%2F2,2)
Region 3: (2,-infinity)
Test the inequality in each region to see if it's part of the solution set.
I'll do the first region and you finish it.
Region 1: (-infinity,-1%2F2)
CHoose a point in the region, not an endpoint,
x=-1
Test the inequality,
2x%5E2%3E+3x%2B2
2%28-1%29%5E2%3E3%28-1%29%2B2
2%281%29%3E-3%2B2
2%3E-1
True so region 1 is part of the solution set.
Continue and test the other two regions.