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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.

 Feb 27, 2020
 #1
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(2x+10)(x+3)<(3x+9)(x+8)

 

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

 

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

 

x^2  + 17x  + 42   >  0      factor  as

 

(x + 14) ( x + 3) > 0

 

Notice  that  if   x < -14   this  is true

 

Notice  that  if x  is  on the  interval (-14, -3)  this is false 

 

And  if x  >  -3  this  is true

 

So....the   solution   is

 

(-inf, -14) U ( -3 , inf )  

 

 

cool cool cool

 Feb 27, 2020

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