Final answer:
To solve the equation 1/6x - 3 = 2 - 3/4x, we can multiply both sides of the equation by the least common multiple (LCM) of 6 and 4, which is 12. Then we can combine like terms, isolate the variable x, and solve for x. The solution to the equation is x = 60/11.
Step-by-step explanation:
To solve the equation 1/6x - 3 = 2 - 3/4x, we need to get rid of the denominators. To do this, we can multiply both sides of the equation by the least common multiple (LCM) of 6 and 4, which is 12. This gives us:
12 * (1/6x) - 12 * 3 = 12 * 2 - 12 * (3/4x)
Simplifying this, we get:
2x - 36 = 24 - 9x
Next, we can combine like terms by adding 9x to both sides:
2x + 9x - 36 = 24 - 9x + 9x
This simplifies to:
11x - 36 = 24
Now, we can isolate the variable x by adding 36 to both sides:
11x - 36 + 36 = 24 + 36
This further simplifies to:
11x = 60
Finally, divide both sides by 11 to solve for x:
x = 60/11
Therefore, the solution to the equation is x = 60/11.