Final answer:
The mathematical sentence for the inequality 'Twice the difference of a number and seven is less than or equal to forty' is 2(x - 7) ≤ 40.
Step-by-step explanation:
To write a mathematical sentence for the given inequality, we can start by translating the words into symbols. 'Twice the difference of a number and seven' can be represented as 2(x - 7). 'is less than or equal to forty' can be represented as ≤ 40. Putting it all together, the mathematical sentence for the inequality is 2(x - 7) ≤ 40, which is option a).