To solve this equation, we can start by simplifying both sides:

x + 1/10 + x + 1/11 + x + 1/12 = x + 1/13 + x + 1/14

Combining like terms:

3x + 1/10 + 1/11 + 1/12 = 2x + 1/13 + 1/14

Now, let's find a common denominator for the fractions on both sides. The least common multiple of 10, 11, and 12 is 660.

Multiplying each fraction by the appropriate factor to get a denominator of 660:

(3x * 660/660) + (1/10 * 66/66) + (1/11 * 60/60) + (1/12 * 55/55) = (2x * 660/660) + (1/13 * 60/60) + (1/14 * 55/55)

Simplifying:

(1980x + 66 + 60 + 55)/660 = (1320x + 60 + 55)/660

Combining like terms:

(1980x + 181)/660 = (1320x + 115)/660

Now, we can cross-multiply:

(1980x + 181) * 660 = (1320x + 115) * 660

Simplifying:

1306800x + 119460 = 871200x + 75900

Subtracting 871200x from both sides:

1306800x - 871200x + 119460 = 75900

Simplifying:

435600x + 119460 = 75900

Subtracting 119460 from both sides:

435600x = 43560

Dividing both sides by 435600:

x = 43560/435600

Simplifying:

x = 1/10

Therefore, the solution to the equation is x = 1/10.