Solving the Equation: 1/6x - 2/3 = 1/5x - 1
In this article, we will solve the equation 1/6x - 2/3 = 1/5x - 1 and find the value of x.
Step 1: Multiply Both Sides by the Least Common Multiple (LCM)
To eliminate the fractions, we need to multiply both sides of the equation by the Least Common Multiple (LCM) of 6, 3, and 5, which is 30.
(30)(1/6x - 2/3) = (30)(1/5x - 1)
This becomes:
5x - 20 = 6x - 30
Step 2: Simplify the Equation
Now, let's simplify the equation by combining like terms:
5x - 20 = 6x - 30
Subtract 5x from both sides:
-20 = x - 30
Add 30 to both sides:
10 = x
Solution
Therefore, the value of x is 10.
Conclusion
In conclusion, we have successfully solved the equation 1/6x - 2/3 = 1/5x - 1 and found the value of x to be 10.
