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Find all solutions to the inequality \(\frac{(2x-7)(x-3)}{x} \ge 0. \)

Please enter in interval notation. 

 Mar 5, 2020
 #1
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(2x - 7) ( x - 3)

____________   ≥  0

        x

 

Note  that  

 

2x - 7    ≥  0    

2x  ≥  7

x   ≥ 7/2

 

So  all  values of  x  ≥ 7/2   will  make the  inequality true

 

And  note  that   when    x  is on the interval    (0 , 3 ] it will also be true

 

And when  x  < 0    it is never true

 

So......the intervals that make this true  are

 

(0, 3 ]  U  [ 7/2, inf)

 

Here's  the  graph to show this  :

 

https://www.desmos.com/calculator/zrszwkjmby

 

 

cool cool cool

 Mar 5, 2020

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