04-12-2017
Mathematics

contestada

The inequality x^2-14x>15 is equivalent to:

(a) -3<x<5
(b) -1<x<15
(c) 3 < x < 5
(d) x<-1 or x>15
(e) x<3 or x>5

And please explain why.

Respuesta :

thewisestudent9 thewisestudent9

07-12-2017

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x^2 - 14x > 15

x^2 - 15x - 15 > 0

(x + 1)(x -15) > 0

If we take a stance and say BOTH POSITIVE, we see

x > -1 OR x > 15

In this case x > 15 is the dominating factor...

If we take a stance and say BOTH NEGATIVE, we see...

x < -1 OR x < 15

In this case x < -1 is the dominating factor...

Now combine the 2 proven factors, we get...

x < -1 OR x > 15

So...

The answer is: D.) x<-1 or x>15

Answer Link

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