SOLUTION: Please show the workings to solve this inequality, many thanks. (x-7)(2x+1)<0

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Question 1021652: Please show the workings to solve this inequality, many thanks.
(x-7)(2x+1)<0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Break up the number line according to the critical points of the function.
x-7=0
x=7
.
.
2x%2B1=0
2x=-1
x=-1%2F2
.
.
So then break up the number line into 3 regions,
Region 1: (-infinity,-1%2F2)
Region 2: (-1%2F2,7)
Region 3: (7,infinity)
Choose a number in each region and test the inequality.
If the inequality is true, the region is part of the solution.
If not, then it's not part of the solution.
Region 1: x=-2
%28-2-7%29%282%28-2%29%2B1%29%3C0
%28-9%29%28-3%29%3C0
27%3C0
False
Region 2: x=0
%280-7%29%282%280%29%2B1%29%3C0
%28-7%29%281%29%3C0
-7%3C0
True
Region 3: x=8
%288-7%29%282%288%29%2B1%29%3C0
%281%29%2817%29%3C0
17%3C0
False
So then the solution region is,
(-1%2F2,7)
.
.
.
Visually, check for when the function is below the x-axis (y%3C0),
.