To solve this equation, we first need to find a common denominator for the fractions on the left side of the equation. The common denominator for 1/3 and 2/3 is 3.

So, the equation becomes:

1/3 + 2/3x = -7

Now, we can combine the fractions:

(1 + 2x)/3 = -7

Next, we can multiply both sides of the equation by 3 to get rid of the denominator:

1 + 2x = -21

Now, we can isolate the variable x by subtracting 1 from both sides:

2x = -22

Finally, we divide by 2 to solve for x:

x = -11

Therefore, the solution to the equation 1/3 + 2/3x = -7 is x = -11.