Solving the Equation 3x - 2/4 + x + 3/2 = x - 1/3 - x - 1/12
In this article, we will solve the equation 3x - 2/4 + x + 3/2 = x - 1/3 - x - 1/12. This equation involves fractions and variables, making it a bit more challenging to solve. But don't worry, we'll break it down step by step.
Simplifying the Equation
First, let's simplify the equation by combining like terms:
3x - 1/2 + x + 3/2 = x - 1/3 - x - 1/12
Next, we can combine the fractions on the left side of the equation:
3x + x - 1/2 + 3/2 = x - 1/3 - x - 1/12
Combine the variables:
4x + 1/2 = x - 1/3 - x - 1/12
Solving for x
Now, let's solve for x. We can start by multiplying both sides of the equation by the least common multiple of the denominators, which is 12:
48x + 6 = 12x - 4 - 12x - 1
Next, we can simplify the equation:
48x + 6 = -5
Subtract 6 from both sides:
48x = -11
Finally, divide both sides by 48:
x = -11/48
Conclusion
The solution to the equation 3x - 2/4 + x + 3/2 = x - 1/3 - x - 1/12 is x = -11/48.
