To solve for x, first distribute the negative sign to the parentheses:

7 1/7 - (6/13) - x = 1 7/13

Next, convert the mixed numbers to improper fractions:

50/7 - 6/13 - x = 20/13

To solve for x, we need to combine like terms and isolate x. First, find a common denominator for 7 and 13, which is 91.

(50/7 13/13) - (6/13 7/7) - x = 20/13

650/91 - 42/91 - x = 20/13

Now, combine the fractions on the left side of the equation:

608/91 - x = 20/13

To isolate x, subtract 608/91 from both sides:

x = 20/13 - 608/91

To add or subtract fractions, the denominators must be the same. Find a common denominator for 13 and 91, which is 91:

x = 140/91 - 608/91

Combine the fractions:

x = (140 - 608) / 91x = -468 / 91

Therefore, x = -468/91.