Let's denote the unknown number as \( x \).
According to your phrase, "the product of a number and two increased by seven," we can express this mathematically as:
\[ 2x + 7 \]
Here, \( 2x \) represents the product of the number \( x \) and 2, and then we add 7 to that product. If you need further assistance or have a specific question about this expression, feel free to ask!