The average of $x+6$, $6x+2$, and $2x+7$ is $4x-7$. What is $x$?
To find the average of three numbers, I need to add them up and divide by three. So I have: $\frac{x+6+6x+2+2x+7}{3}=4x-7$. I can simplify the numerator by combining like terms: $\frac{9x+15}{3}=4x-7$. To get rid of the fraction, I can multiply both sides by three: $9x+15=12x-21$. Then I can subtract $9x$ from both sides: $15=3x-21$. Next, I can add $21$ to both sides: $36=3x$. Finally, I can divide both sides by three to get $x$: $x=12$. 