Solving Linear Equations in One Variable

The number $299$ is divided into two parts in the ratio $5:8$. The product of the numbers is _____.

Solve for $x$: $6\left(3x+2\right)-5\left(6x-1\right)=6\left(x-3\right)-5\left(7x-6\right)+12x$

If $\frac{1}{3}$ of a number is $10$ less than the original number, then the number is _____.

A number is $56$ greater than the average of its third, quarter and one-twelfth. Find the number.

Solve for $x:$

$\frac{3x+1}{16}+\frac{2x-3}{7}=\frac{x+3}{8}+\frac{3x-1}{14}$