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Find all $p$ which satisfy both the inequalities $0\ge 54p-144$ and $0>12-20p$. Express your answer in interval notation, reducing any fractions in your answer.

 Apr 14, 2018
 #1
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Find all  \(p\)  which satisfy both the inequalities  \(0\ge 54p-144\)  and  \(0>12-20p\) .

Express your answer in interval notation, reducing any fractions in your answer.

 

0  ≥  54p - 144

                           Add  144  to both sides of the inequality.

144  ≥  54p

                           Divide both sides by  54 .

144/54  ≥  p

 

8/3  ≥  p

 

 

0  >  12 - 20p

                           Add  20p  to both sides.

20p  >  12

                           Divide both sides by  20 .

p  >  12/20

 

p  >  3/5

 

We can combine   8/3  ≥  p   and   p  >  3/5   to get...

 

8/3  ≥  p  >  3/5    which is the same as...

 

3/5  <  p  ≤  8/3    And  8/3  is greater than  3/5  so this is valid.

 

In interval notation, it is   (3/5, 8/3]

 Apr 14, 2018

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