Final answer:
To find the number, set up an equation based on the given information and solve for x.
Step-by-step explanation:
To find the number, we can set up an equation based on the given information. Seven times the difference of a number x and 2 is the same as two times the number x increased by 21. Mathematically, this can be expressed as 7(x-2) = 2x + 21. Now, we can solve for x:
7x - 14 = 2x + 21 (distribute the 7)
7x - 2x = 21 + 14 (combine like terms)
5x = 35
x = 7
Therefore, the number is 7.