SOLUTION: What is the answer to this quadratic inequality. 2x^2<9x+18

Question 1200711: What is the answer to this quadratic inequality. 2x^2<9x+18
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What is the answer to this quadratic inequality. 2x^2<9x+18
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The answer depends on the question.
It might be "how many 2's are in it?"
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If you want to solve for x, say, "Solve for x."
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2x^2<9x+18
2x^2- 9x - 18 < 0
(x - 6)*(2x - 3) < 0
x - 6 < 0
x < 6
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2x - 3 < 0
x < 3/2
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---> x < 6
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Ignore the solution from the other tutor; his process is faulty and his answer is wrong.

It's a quadratic inequality. Just as with a quadratic equation, move terms to get "0" on one side:

Factor the quadratic:

The value of the expression is 0 only at x=-3/2 and x=6; the sign of the evaluated expression can only change at those two values of x. So there are three intervals we need to check to see on which of them the inequality is satisfied: (-infinity,-3/2), (-3/2,6), and (6,infinity).

One standard way to do this is to choose a test value in each interval. I leave it to you to do that if you want.

Another easier way to determine the intervals on which the inequality is satisfied is to know that the graph of the quadratic is an upward-opening parabola; since the inequality is for the expression value to be negative, the solution set is the interval between the two zeros: (-3/2,6).

ANSWER: (-3/2,6)

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