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Find all x that satisfy the inequality \((2x+10)(x+3)<(3x+9)(x+8)\). Express your answer in interval notation.

 Jul 26, 2019
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(2x + 10) (x + 3)  <  (3x + 9) (x + 8)      simplify

 

2x^2 +10x + 6x + 30 <  3x^2 + 9x + 24x + 72

 

2x^2 + 16x + 30 < 3x^2 + 33x + 72

 

0   <  x^2 + 17x + 42

 

x^2 + 17x + 42   >  0         factor

 

(x + 14) ( x + 3)   > 0 

 

Set each factor to 0  and solve for  x and we have that  x  = -14    and  x  = -3......

So....we have the following posible solution intervals   ... (-infinity, -14)   or (-14, -3)  or (-3, infinity)

 

When  the interval  on x  is  from

 

(- infinity, -14)    ⇒      (x + 14) (x + 3)   is > 0

( -14, -3)  ⇒  (x + 14) ( x + 3)  is  < 0

(-3, infinity)  ⇒  (x + 14) (x + 3)  is > 0

 

So.....the solution intervals  lie   on  ( -infinity , -14) U ( -3 , infinity )  

 

 

cool cool cool

 Jul 26, 2019

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