please help with x+1/3=5-x+2/7?

x + 1/3 = 5 - x + 2/7
x + 1/3 + x = 5 - x + 2/7 + x
2x + 1/3 = 5 + 2/7
2x + 1/3 = 37/7
2x + 1/3 - 1/3 = 37/7 - 1/3
2x = 118/21
2x/2 = (118/21) / 2
x = 59/21

As given , question MUST be read as :-
x + (1/3) = 5 - x + (2/7)
2x = 5 + (2/7) - (1/3)
2x = 5 + 6/21 - 7/21
2x = 5 - 1/21
2x = 4 + 20/21
x = 4 + 10/21
x = 4 10/21

If you mean :-
(x + 1) / 3 = 5 - (x + 2) / 7
7(x + 1) = 105 - 5(x + 2)
7x + 7 = 105 - 5x - 10
7x + 7 = 95 - 5x
12x = 88
x = 22 / 3

PS
Remember to use brackets to avoid confusion.

(x + 1)/3 = 5 - (x + 2)/7
21[(x + 1)/3] = 21[5 - (x + 2)/7]
7(x + 1) = 105 - 3(x + 2)
7x + 7 = 105 - 3x - 6
7x + 3x = 105 - 6 - 7
10x = 92
x = 92/10
x = 46/5 (9.2)

x+1/3=5-x+2/7
x+x+1/3=5+2/7
2x=5+2/7-1/3
2x=37/7-1/3
2x=111/21-7/21
2x=104/21
x=104/21 x 1/2
x=104/48
x=2 8/48
x=2 1/6

x + 1/3 = 5 - x + 2/7

Add x on both sides.
2x + 1/3 = 5 + 2/7.

Subtract 1/3 from both sides.
2x = 5 + 2/7 - 1/3.

Divide both sides by 2.
x = 5/2 + 2/14 - 1/6.

The LCM of 2, 14 and 6 is 42. So,
x = 5*21/42 + 2*3/42 - 1*7/42.
x = 104/42.

In simplest terms,
x = 52/21.

:)

I concur with the first person (although in a different form)

the answer is 52/21 or 2 10/21

get the x's on the left and everything else on the rigth side.

x+x=5+2/7-2/3

thats:
2x = 97/21
x = 97/42

add x to both sides:

2x + 1/3 = 5 + 2/7

take 1/3 from both sides:

2x = 118/21

divide both sides by 2:

x = 59/21

x+1/3=5-x+2/7
x+x=5+2/7-1/3
2x=37/7-1/3
2x=104/21
x=104/42
x=52/21
x=2 10/21
Ans: 52/21 or 2 10/21

x + 1/3 = 5 - x + 2/7
x + x = 5 + 2/7 -1/3 transpose
2x = (105 + 6 - 7) / 21
2x = 104/21
x = 104/ 2(21)
x = 104/42
x = 2 20/42 or 2 10/21