A number is such that when it is added to it, the result is the same as multiplying the number by 3 and subtracting 7 from the number. What is the number?

Let the number be $x$.

"A number is such that when it is added to it..."
This means $x + x$, which simplifies to $2x$.

"...the result is the same as multiplying the number by 3 and subtracting 7 from the number."
"Multiplying the number by 3" is $3x$.
"Subtracting 7 from the number" means $3x - 7$.

The problem states that the result from Step 2 is the same as the result from Step 3.

Subtract $3x$ from both sides of the equation:

Multiply both sides by -1:

The equation is $2x = 3x - 7$.
The number is 7.