$$\frac{p-1}{2}+\frac{2p+5}{3}=7$$
$p=5$
$$3\left(p-1\right)+2\left(2p+5\right)=42$$
$$3p-3+2\left(2p+5\right)=42$$
$$3p-3+4p+10=42$$
$$7p-3+10=42$$
$$7p+7=42$$
$$7p=42-7$$
$$7p=35$$
$$p=\frac{35}{7}$$
$$p=5$$
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