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How many integers satisfy the inequality x(3x-4)<= 20?

 Dec 6, 2020
 #1
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x(3x - 4)  ≤ 20

 

3x^2  - 4x  - 20  ≤   0

 

(3x   - 10)  ( x + 2) ≤   0       (1)

 

Set  factors to 0   and solve  for  x to  find the  critical points

 

x = 10/ 3      x  =  -2

 

We have  three intervals  that we can test

 

(-inf, -2 ]   ,  [ -2, 10/3 ]     and [ 10/3, inf ) 

 

  Picking an x  in each interval  to test in (1)  shows that the  solution      =  [ -2, 10/3  ]   

 

 

cool cool cool

 Dec 6, 2020

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