To solve this equation, we need to simplify the expression on the left side:

x - [ 17/2 - (-3 / 7 + 5 /3) ] = -1 / 3

First, let's simplify the expression inside the square brackets:

-3 / 7 + 5 / 3

To add these fractions, we need to find a common denominator. The common denominator for 7 and 3 is 21. So, we can rewrite the expression as:

(-3 * 3) / (7 * 3) + (5 * 7) / (3 * 7)
= -9 / 21 + 35 / 21

Now, we can add the fractions:

-9 / 21 + 35 / 21
= (35 - 9) / 21
= 26 / 21

Now, let's substitute this value back into the original equation:

x - [ 17/2 - 26 / 21 ] = -1 / 3

Next, let's simplify the expression inside the square brackets:

17/2 - 26 / 21

To subtract these fractions, we need to find a common denominator. The common denominator for 2 and 21 is 42. So, we can rewrite the expression as:

(17 * 21) / (2 * 21) - 26 / 21
= 357 / 42 - 26 / 21

Now, we can subtract the fractions:

357 / 42 - 26 / 21
= (357 * 2) / (42 * 2) - 26 / 21
= 714 / 84 - 26 / 21
= 8.5 - 1.2381
= 7.2619

Now, let's substitute this value back into the original equation:

x - 7.2619 = -1 / 3

To isolate x, we can add 7.2619 to both sides:

x - 7.2619 + 7.2619 = -1 / 3 + 7.2619
x = 7.2619 - 1 / 3

To add a fraction and a decimal, we need to convert the fraction to a decimal:

x = 7.2619 - 0.3333
x = 6.9286

Therefore, the solution to the equation is x = 6.9286.