Question 95640
I have worked your problem two different ways and find that the answer that you give (x = 7) is just not possible.
In the first place, to remove any ambiguity on the problem statement, please use parentheses! Why? Because...
3/7x can be interpreted to mean either: {{{(3/7)x}}} or {{{3/7x}}}
Whereas, (3/7)x can be interpreted only as {{{(3/7)x}}}

In the second place, the only way that I can get the answer that you give, (x = 7) is if the problem starts with {{{(-3/7)x}}}, so...
{{{(-3/7)x+2 = (4/7)x-5}}} Multiply through by the LCD of 7.
{{{7((-3/7)x+2) = 7((4/7)x-5)}}} Simplify.
{{{(-3x+14) = (4x-35)}}} Add 3x to both sides.
{{{14 = 7x-35}}} Add 35 to both sides.
{{{49 = 7x}}} Finally, divide both sides by 7.
{{{7 = x}}} or {{{x = 7}}}

Please check the original problem for a possible missing negative sign!