For what values of k and c does the equation 5(x-2)+12 = kx+c have infinitely many solutions?

Simplify the left side: $5(x - 2) + 12 = 5x - 10 + 12 = 5x + 2$. The equation is $5x + 2 = kx + c$. It has infinitely many solutions only when both sides are identical expressions, so $k = 5$ and $c = 2$, choice A. Choice B ($k = 5$, $c = 6$) matches the coefficient but not the constant, giving $2 = 6$, so no solution. Choice C ($k = 6$, $c = 2$) gives exactly one solution, $x = 0$. Choice D ($k = 5$, $c = -2$) has a sign error and gives $2 = -2$, no solution. Both the coefficient and constant must match.