+612 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.
+9479 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]
