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# Algebra... Help~

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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.

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

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]

hectictar  Apr 14, 2018

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