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

0 > 12 - 20p

144 ≥ 54p divide both sides by 54

144/54 ≥ p

8/3 ≥ p

p ≤ 8/3

20p > 12 divide both sides by 20

p > 12/20

p > 3/5

The answer is :

p = (3/5, 8/3 ]