Solving the Equation: 1/5x - 5/6 - 2/3x = 1/4 - 3/5x + 2/3
In this article, we will solve the equation 1/5x - 5/6 - 2/3x = 1/4 - 3/5x + 2/3. This equation involves fractions and variables, which can make it a bit more challenging to solve. However, with the right steps, we can simplify the equation and find the value of x.
Step 1: Combine Like Terms
First, let's combine the like terms on both sides of the equation.
Left Side:
1/5x - 2/3x = -1/2x (Combine the x terms) -5/6 (keep the constant term as is)
Right Side:
1/4 - 3/5x + 2/3 (keep the terms as is)
So, the equation becomes:
-1/2x - 5/6 = 1/4 - 3/5x + 2/3
Step 2: Add 5/6 to Both Sides
To get rid of the negative term on the left side, we'll add 5/6 to both sides of the equation.
-1/2x = 1/4 - 3/5x + 2/3 + 5/6 -1/2x = 1/4 + 2/3 + 5/6 - 3/5x
Step 3: Simplify the Right Side
Now, let's simplify the right side of the equation.
1/4 + 2/3 + 5/6 = 47/60 (Simplify the fractions)
So, the equation becomes:
-1/2x = 47/60 - 3/5x
Step 4: Solve for x
To solve for x, we'll add 3/5x to both sides of the equation.
-1/2x + 3/5x = 47/60 (2/10)x + (3/5)x = 47/60 (13/10)x = 47/60
Now, multiply both sides by 10 to eliminate the fractions.
13x = 47
Divide both sides by 13 to solve for x.
x = 47/13 x = 3.69 (approx.)
And that's it! We've solved the equation 1/5x - 5/6 - 2/3x = 1/4 - 3/5x + 2/3. The value of x is approximately 3.69.
