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x^2+3x<28

Guest Apr 7, 2015

Best Answer 

 #1
avatar+88898 
+10

x^2+3x<28      subtract 28 from each side

x^2 + 3x - 28 < 0      factor

(x + 7) (x - 4) < 0     

Our answers will come from either these two invervals {- ∞, -7)  and (4, ∞ )

Or, this interval  (-7 , 4)

Let's pick 0 in the last interval and test it in the inequality

(0 + 7) ( 0 - 4)  <  0    ???

(7) (-4) < 0  ???

-28 < 0     and this is true

So......the answer is   x = (-7 ,4)

Here's a graph of   y = x^2 + 3x - 28   ..... https://www.desmos.com/calculator/rq4hlo0pr0

Notice that the graph is < 0  on the interval (-7, 4)

 

   

CPhill  Apr 7, 2015
 #1
avatar+88898 
+10
Best Answer

x^2+3x<28      subtract 28 from each side

x^2 + 3x - 28 < 0      factor

(x + 7) (x - 4) < 0     

Our answers will come from either these two invervals {- ∞, -7)  and (4, ∞ )

Or, this interval  (-7 , 4)

Let's pick 0 in the last interval and test it in the inequality

(0 + 7) ( 0 - 4)  <  0    ???

(7) (-4) < 0  ???

-28 < 0     and this is true

So......the answer is   x = (-7 ,4)

Here's a graph of   y = x^2 + 3x - 28   ..... https://www.desmos.com/calculator/rq4hlo0pr0

Notice that the graph is < 0  on the interval (-7, 4)

 

   

CPhill  Apr 7, 2015

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