#### Answer

c=-5

#### Work Step by Step

$\frac{c+1}{c-2}=\frac{4}{7}$ cross multiply
$7(c+1)=4(c-2)$ distributive property
$7c+7=4c-8$ subtract 4c from both sides; subtract 7 from both sides
$7c+7-4c-7=4c-8-4c-7$ combine like terms
$3c=-15$ divide both sides by 3
$3c\div3=-15\div3$ simplify
$c=-5$