Answer
$p\gt\frac{3}{2}$
Work Step by Step
Write out equation
$\frac{2}{3}(5p-3)\gt\frac{3}{4}(2p+1)$
Give both fraction coefficients the same common denominators
$\frac{8}{12}(5p-3)\gt\frac{9}{12}(2p+1)$
Distribute
$\frac{40}{12}p-\frac{24}{12}\gt\frac{18}{12}p+\frac{9}{12}$
Combine like terms
$\frac{22}{12}p\gt\frac{33}{12}$
Isolate p by multiplying the entire inequality by $p$'s reciprocal
$\frac{12}{22}(\frac{22}{12}p\gt\frac{33}{12})$
$p\gt\frac{33}{22}$
Simplify
$p\gt\frac{3}{2}$
