Solving the Equation 5/6(1/3x-1/5)=3x+3 1/3
In this article, we will solve the equation 5/6(1/3x-1/5)=3x+3 1/3. This equation involves fractions and mixed numbers, making it a bit challenging. However, with the right steps, we can simplify and solve for x.
Step 1: Simplify the Left-Hand Side
First, let's simplify the left-hand side of the equation:
5/6(1/3x-1/5) = ?
To evaluate this expression, we need to follow the order of operations (PEMDAS):
- Multiply 1/3x and -1/5 by 5/6:
(5/6)(1/3x) = 5x/18 (5/6)(-1/5) = -1/6
So, the left-hand side becomes:
5x/18 - 1/6
Step 2: Simplify the Right-Hand Side
Now, let's simplify the right-hand side of the equation:
3x+3 1/3 = ?
We can rewrite the mixed number 3 1/3 as an improper fraction:
3 1/3 = 10/3
So, the right-hand side becomes:
3x + 10/3
Step 3: Equate the Two Expressions
Now that we have simplified both sides of the equation, we can equate them:
5x/18 - 1/6 = 3x + 10/3
Step 4: Solve for x
To solve for x, we can start by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 18:
(5x/18 - 1/6) × 18 = (3x + 10/3) × 18
This gives us:
5x - 3 = 54x + 60
Now, let's subtract 54x from both sides:
-49x - 3 = 60
Next, add 3 to both sides:
-49x = 63
Finally, divide both sides by -49:
x = -63/49
x = -27/7
Therefore, the value of x is -27/7.
Conclusion
In this article, we have successfully solved the equation 5/6(1/3x-1/5)=3x+3 1/3. We started by simplifying both sides of the equation, equated the two expressions, and finally solved for x. The solution is x = -27/7.
