To solve this equation, we need to first convert the mixed numbers into improper fractions.

8 5/13x = 4 5/26

First, convert 8 into an improper fraction:
8 = 8/1

Now, convert the mixed numbers into improper fractions:
5/13 = (13 5 + 5) / 13 = 70 / 13
5/26 = (26 5 + 5) / 26 = 135 / 26

Now, rewrite the equation using the improper fractions:
(8 + 70/13)x = 4 + 135/26

(8 + 70/13)x = 4 + 135/26

Now, add the fractions on the right side:
(8 + 70/13)x = 4 + (135/26) is he same as 4 + (5 + 10/26)

(8 + 70/13)x = 9 + 10/26

Now, subtract 8 from both sides:
70/13x = 1 + 10/26

Now, simplify by finding a common denominator:
70/13x = 1 + 5/13

Now, subtract the fractions on the right side:
70/13x = 13/13 + 5/13
70/13x = 18/13

Now, solve for x by multiplying both sides by 13/70:
x = 18/13 * 13/70
x = 18/70
x = 9/35

Therefore, the solution to the equation is x = 9/35.