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Find all values of \(x\) that satisfy \(x(x+7.5) > 38.5\). Give your answer in interval notation.

 Jul 23, 2019
 #1
avatar+683 
+3

the answer is 11 < x < 3.5

 Jul 23, 2019
edited by travisio  Jul 23, 2019
edited by travisio  Jul 23, 2019
 #2
avatar+102399 
+3

x ( x + 7.5) > 38.5

 

x^2 + 7.5x > 38.5

 

x^2 + 7.5x - 38.5 > 0    multiply through by 2

 

2x^2 + 15x - 77 > 0     factor

 

(2x  - 7) ( x + 11) > 0    set  each factor to 0

 

2x - 7  = 0             x + 11 = 0

2x  = 7                   x  = - 11

x  = 7/2

 

We have three possible intervals that make the original inequality true

 

(-infinity, -11)  or  ( -11, 7/2)  or  (7/2, infinity)

 

Testing 0  in the middle interval makes the inequality false

 

So....the two intervals that make the original inequality true are

 

(-infinity, -11) U ( 7/2, infinity )

 

 

cool cool cool

 Jul 23, 2019

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