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 + 93x = 3x = 1
Therefore, the solution to the equation is x = 1.
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.