(x-2):6+x:2=(5x-2):9

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To solve this equation, we first need to simplify both sides:

Left side:
(x-2)/6 + x/2

To add fractions, we need a common denominator which in this case is 6. So we need to rewrite x/2 as x*3/6.

Now the left side becomes:
(x-2)/6 + 3x/6
= (x-2 + 3x) / 6
= (4x - 2) / 6
= (2(2x-1)) / 6
= (2x-1) / 3

Right side:
(5x-2)/9

Now our equation becomes:
(2x-1)/3 = (5x-2)/9

To get rid of the fractions, we can multiply both sides by 9 (LCM of the denominators):
9(2x-1) = 3(5x-2)

Expanding both sides:
18x - 9 = 15x - 6

Now we isolate x by moving the x terms to one side and the constants to the other:
18x - 15x = -6 + 9
3x = 3
x = 1

Therefore, the solution to the equation is x = 1.