#### Answer

The Democratic candidate received 2386 votes.

#### Work Step by Step

Let $d$ be the Democrat votes. Independent votes is $d-272$.
Incumbent+Democrat+Independent=Total Votes
$14,000+d+d-272=18,500$ $\longrightarrow$combine like terms
$13728+2d=18500$ $\longrightarrow$addition property
$13728+2d-13728=18500-13728$ $\longrightarrow$combine lie terms
$2d=4772$ $\longrightarrow$multiplication property
$2d\div2=4772\div2$ $\longrightarrow$simplify
$d=2386$