Hi there.

The answer does not seem right. If I read properly what you wrote, you are saying that
(x + 1) / 3 + (x + 2) / 7 = 2

If we multiply both sides by 21, we get this:

7 ( x + 1) + 3 ( x + 2 ) = 2 (21)

Now we can distribute the factors and solve for x:

7x + 7 + 3x + 6 = 42
10x = 42 - 6 - 7
10x = 29
x = 29 / 10.

That's a different answer than your book gives. So either I am misunderstanding the initial equation you sent, or the book is wrong.

If it was right, we could plug in x = 10/21 (the answer the book gives) and work out the left hand side of the equation and see if it makes 2 (the right hand side):

(10/21 + 1) / 3 + (10/21 + 2) / 7
= (31/21) / 3 + (52 / 21) / 7
= 31 / 63 + 52 / 147
= 31 (7) / 441 + 52 (3) / 441
= (217 + 156) / 441
= 373 / 441. Definitely not equal to 2.

Here's proof that x = 29/10 works though:

(29/10 + 1) / 3 + (29/10 + 2) / 7
= (39/10) / 3 + (49/10) / 7
= 39/30 + 49/70
= 13/10 + 7/10
= 20/10
= 2.

Cheers.
Stephen La Rocque.