SOLUTION: Need to solve the following inequalities by hand. Please help me, thank you! (x-7)(2x+1)<0

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Question 1021445: Need to solve the following inequalities by hand. Please help me, thank you!
(x-7)(2x+1)<0
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
The critical values are easily found because left hand member is in factored form. They are -1%2F2 and 7.

The left member represents a parabola opening upward, having vertex as a minimum, so knowing this shape and typical relationship to the axes will tell you what you want; that the inequality will be satisfied BETWEEN BUT EXCLUSIVE to .... -1%2F2%3Cx%3C7.

The other way to find the answer is to pick points on x in the three intervals which the critical values form, and check for which of them satisfy the inequality.