Solve for $x$: $\frac{x}{3}+\frac{x}{4}=14$.
I see that this equation involves fractions, so I want to clear the denominators by multiplying both sides by a common multiple. The least common multiple of 3 and 4 is 12, so I multiply both sides by 12: $12\cdot\frac{x}{3}+12\cdot\frac{x}{4}=12\cdot 14$. This simplifies the equation by canceling out the fractions: $4x+3x=168$. Now I can combine the like terms and solve for $x$: $7x=168$. Dividing both sides by 7, I get $x=\frac{168}{7}=24$. 