Solving the Equation: 1/4x + 2/3x - x = 3/5x - 1/2
In this article, we will solve the equation 1/4x + 2/3x - x = 3/5x - 1/2. To solve this equation, we will follow the steps of combining like terms and isolating the variable x.
Step 1: Combine Like Terms
First, let's combine the like terms on the left-hand side of the equation:
1/4x + 2/3x - x = ?
To combine these terms, we need to find a common denominator, which is 12x. So, we can rewrite the terms as:
(3x + 8x - 12x) / 12 = ?
Simplifying the numerator, we get:
(-x) / 12
So, the left-hand side of the equation becomes:
-x / 12
Step 2: Equate and Simplify
Now, let's equate the simplified left-hand side with the right-hand side of the equation:
-x / 12 = 3/5x - 1/2
To simplify, we can multiply both sides of the equation by 60 (the least common multiple of 12, 5, and 2) to eliminate the fractions:
-5x = 18x - 30
Step 3: Isolate the Variable
Now, let's isolate the variable x by adding 5x to both sides of the equation:
-5x + 5x = 18x - 30 + 5x
This simplifies to:
0 = 23x - 30
Subtracting 23x from both sides gives us:
-23x = -30
Dividing both sides by -23, we finally get:
x = 30/23
Conclusion
Therefore, the solution to the equation 1/4x + 2/3x - x = 3/5x - 1/2 is x = 30/23.
