What is 7+7x; 7 (x + 1/7

Is 7 + 7x equivalent to 7 (x + 1/7) ?

Answer

Let's assume for the moment that 7 + 7x is indeed equivalent (equal in value, amount, meaning, etc.) to 7 (x + 1/7); therefore, ...

7 + 7x = 7 (x + 1/7)

7 + 7x = 7x + 7 (1/7)

7 + 7x = 7x + 1

7x + 7 = 7x + 1

Now, subtracting 7x from both sides, we get:

7x - 7x + 7 = 7x - 7x + 1

(7 - 7) x + 7 = (7 - 7) x + 1

(0) x + 7 = (0) x + 1 Which leads to the erroneous, false statement:

7 = 1 (As we know, 7 >1)

Therefore, ...

7 + 7x is NOT equivalent (equal in value, amount, meaning, etc.) to 7 (x + 1/7) !

Also, think about this: How can 7 more than 7 times a number x be equivalent to 1 more than 7 times that same number x?, i. e., how can 7x + 7 = 7x + 1?! Answer: It can't!