Answer
The number is $10$.
Work Step by Step
Let $x$ be the unknown number.
Then, the difference of a number and $7$ is $x-7$.
Translating $``\text{four times the difference of a number and 7}"$ yields $4(x-7)$.
Thus, the equation needed to find the unknown number is:
$$4(x-7)=12$$
Solve the equation:
$$\begin{align*}
\frac{4(x-7)}{4}&=\frac{12}{4} &\text{Divide 4 to both sides.}\\
x-7&=3 &\text{Simplify.}\\
x-7+7&=3+7 &\text{Add 7 to both sides.}\\
x&=10 &\text{Simplify.}
\end{align*}$$
Thus, the number is $10$.
