To solve the equation, we need to isolate the variable x.

First, let's simplify the left side of the equation by finding a common denominator for 2/3 and 1/2. The common denominator is 6.

2/3 = (2/3) * (2/2) = 4/6
1/2 = (1/2) * (3/3) = 3/6

Now, the equation becomes:

4/6 * x + 3/6 = 1/10

Next, let's combine the fractions on the left side:

(4/6)x + 3/6 = 1/10

Now, let's subtract 3/6 from both sides of the equation to isolate the term with x:

(4/6)x = 1/10 - 3/6

To subtract fractions, we need a common denominator. The common denominator is 30.

1/10 = (1/10) * (3/3) = 3/30
3/6 = (3/6) * (5/5) = 15/30

Now, the equation becomes:

(4/6)x = 3/30 - 15/30

Simplifying the right side:

(4/6)x = -12/30

Now, let's simplify the left side by dividing both the numerator and denominator of 4/6 by their greatest common divisor, which is 2:

(2/3)x = -12/30

Now, let's multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:

(2/3)x * (3/2) = (-12/30) * (3/2)

Simplifying both sides:

(2/3) * (3/2) * x = -36/60

Multiplying fractions:

(6/6) * x = -36/60

Simplifying:

1 * x = -36/60

x = -36/60

The solution is x = -36/60, which can be simplified to x = -3/5.