Question 355844: Hi, I'm being asked to solve the inequality and graph on a number line. I'm new to this, so I'm wondering do I treat the inequality as an equation and complete the square?
x^2 + x - 9 > 3
x^2 + x + .25 > 12
(x + .5)^2 > 12
x > -.5 +/- sqrt(12)
Would this be correct? I'm getting x > 2.96 and x > -3.96, and not sure how I would put this on a number line. Any guidance you can provide is greatly appreciated!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! x^2 + x - 9 > 3
x^2 + x + .25 > 12.25 (not 12)
(x + .5)^2 > 12.25
x > -.5 +/- 3.5
Would this be correct? I'm getting x > 2.96 and x > -3.96
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x^2 + x - 9 > 3
x^2 + x - 12 > 0
(x+4)*(x-3) > 0
For the product to be > 0, the terms have to have the same signs.
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(x+4) & (x-3) > 0 --> x > 3 (that makes it > -4)
or,
(x+4) & (x-3) < 0 --> x < -4 (which is less than +3)
--> x < -4 or x > 3
--> x is all real numbers except from -4 to +3 inclusive
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