Final answer:
The phrase '7 minus 2 times the difference of the number and 4' is expressed mathematically as 7 - 2(x - 4), which simplifies to 15 - 2x.
Step-by-step explanation:
To translate the phrase "7 minus 2 times the difference of the number and 4" to a mathematical expression, we start by identifying the number which is represented by the variable x. Next, we recognize that 'difference of the number and 4' means x - 4. The phrase '2 times' indicates multiplication, so '2 times the difference of the number and 4' is 2(x - 4).
Bringing it all together, we get the expression 7 - 2(x - 4). To simplify, we firstly distribute the 2 into the parentheses, obtaining 7 - 2x + 8. Simplifying further by combining like terms, we get 15 - 2x as the simplified expression.