Solving the Equation: 4/5x - 3 = x - 1/3
In this article, we will solve the equation 4/5x - 3 = x - 1/3. This equation involves fractions and variables, but don't worry, we'll break it down step by step.
Step 1: Simplify the equation
First, let's simplify the equation by combining like terms:
4/5x - 3 = x - 1/3
We can start by getting rid of the fraction on the right-hand side of the equation. To do this, we'll multiply both sides of the equation by 3 to eliminate the fraction:
3(4/5x - 3) = 3(x - 1/3)
This gives us:
24/5x - 9 = 3x - 1
Step 2: Isolate the variable
Next, we'll isolate the variable x by adding 9 to both sides of the equation:
24/5x - 9 + 9 = 3x - 1 + 9
This gives us:
24/5x = 3x + 8
Step 3: Solve for x
Now, we'll solve for x by subtracting 3x from both sides of the equation:
24/5x - 3x = 8
This gives us:
(24/5 - 3)x = 8
Next, we'll simplify the left-hand side of the equation:
(-3/5)x = 8
Finally, we'll divide both sides of the equation by -3/5 to solve for x:
x = -8 / (3/5)
x = -8 * (5/3)
x = -40/3
Therefore, the solution to the equation 4/5x - 3 = x - 1/3 is x = -40/3.
