Solving the Equation 5x/4 - x - 1/2 = x - 1/3
In this article, we will solve the equation 5x/4 - x - 1/2 = x - 1/3. This equation involves fractions and variables, making it a challenging problem to solve. However, with the right steps and techniques, we can find the value of x.
Step 1: Simplify the Equation
First, let's simplify the equation by getting rid of the fractions. We can do this by finding the least common multiple (LCM) of the denominators, which are 4, 2, and 3. The LCM is 12, so we can multiply both sides of the equation by 12 to eliminate the fractions.
12(5x/4 - x - 1/2) = 12(x - 1/3)
Expanding the equation, we get:
15x - 12x - 6 = 12x - 4
Step 2: Combine Like Terms
Next, let's combine like terms on both sides of the equation.
-3x - 6 = 12x - 4
Step 3: Add 3x to Both Sides
Now, let's add 3x to both sides of the equation to get rid of the negative term.
-6 = 15x - 4
Step 4: Add 4 to Both Sides
Next, let's add 4 to both sides of the equation to get:
-2 = 15x
Step 5: Divide by 15
Finally, let's divide both sides of the equation by 15 to solve for x.
x = -2/15
Conclusion
Therefore, the value of x is -2/15. We have successfully solved the equation 5x/4 - x - 1/2 = x - 1/3 using the steps outlined above.
