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What is 1/6x - 3 = 2 - 3/4x

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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.

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