To solve this equation, let's first simplify both sides of the equation separately.

On the left side, we have:

1/3 x 5/7 : x

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we have:

(1/3 x 5/7) * (1/x)

Multiplying the numerators and denominators separately, we get:

(1 * 5) / (3 * 7) * (1/x)

5/21 * (1/x)

Now, let's simplify the right side of the equation:

2/5 + 3/10

To add fractions, we need a common denominator. The least common multiple of 5 and 10 is 10. So, we can rewrite the fractions with a common denominator:

(2/5) * (2/2) + (3/10) * (1/1)

4/10 + 3/10

Now, we can add the fractions:

(4 + 3) / 10

7/10

Now, let's rewrite the equation with the simplified expressions:

5/21 * (1/x) = 7/10

To solve for x, we can cross multiply:

5/21 * 10 = 7 * (1/x)

50/21 = 7/x

To isolate x, we can multiply both sides of the equation by x:

x * (50/21) = 7

Now, divide both sides by 50/21:

x = 7 / (50/21)

To divide by a fraction, we multiply by its reciprocal:

x = 7 * (21/50)

Multiplying the numerators and denominators separately, we get:

x = (7 * 21) / (50)

x = 147/50

Therefore, the solution to the equation is x = 147/50.