To solve this equation, we need to first find a common denominator for the fractions.

First, let's simplify the fractions:
1/3 = 4/12
7/12 = 7/12
1/4 = 3/12

Now, we can rewrite the equation as:
4/12x + 3/12x = 7/12

Combining the fractions on the left side, we get:
7/12x = 7/12

Now, multiply both sides by 12 to get rid of the denominator:
7x = 7

Finally, divide both sides by 7 to solve for x:
x = 1

So, the solution to the equation is x = 1.