To solve these equations, we will simplify and isolate the variable on one side of the equation.

4. (x-250)/6 = 43 - 22x3
First, we simplify the right side of the equation:
(x-250)/6 = 43 - 66x
Next, we multiply both sides of the equation by 6 to eliminate the fraction:
x - 250 = 258 - 396x
Now, we combine like terms:
397x = 508
Finally, we divide both sides of the equation by 397 to solve for x:
x = 508/397

5. 2x + 3x + 5x = 1030
First, we combine like terms on the left side of the equation:
10x = 1030
Next, we divide both sides of the equation by 10 to solve for x:
x = 103

6. 15x - 35x + 50x = 120
First, we combine like terms on the left side of the equation:
30x = 120
Next, we divide both sides of the equation by 30 to solve for x:
x = 4

7. (1/2)x + (1/6)x + (1/3)x = 2023
First, we find a common denominator for the fractions on the left side of the equation, which is 6:
(3/6)x + (1/6)x + (2/6)x = 2023
Next, we combine like terms on the left side of the equation:
(6/6)x = 2023
Now, we simplify the left side of the equation:
x = 2023

8. 165 - (35/(x+3))x19 = 13
First, we simplify the left side of the equation:
165 - (35/(x+3))x19 = 13
165 - (35/((x+3)/1))x19 = 13
165 - (35/1)(19/(x+3)) = 13
165 - (665/(x+3)) = 13
Next, we subtract 165 from both sides of the equation:
- (665/(x+3)) = -152
Now, we multiply both sides of the equation by (x+3) to eliminate the fraction:
-665 = -152(x+3)
Next, we distribute -152 on the right side of the equation:
-665 = -152x - 456
Now, we add 456 to both sides of the equation:
-209 = -152x
Finally, we divide both sides of the equation by -152 to solve for x:
x = -209/-152
x = 1.37