Solving the Equation: 1/3 - x/3 = 7x/12 + 5/4
In this article, we will solve the equation 1/3 - x/3 = 7x/12 + 5/4. To do so, we will follow the standard procedure for solving linear equations with fractions.
Step 1: Simplify the Equation
First, let's simplify the equation by combining the fractions on the right-hand side:
1/3 - x/3 = 7x/12 + 5/4 = 7x/12 + 15/12 = (7x + 15)/12
So, the simplified equation is:
1/3 - x/3 = (7x + 15)/12
Step 2: Cross-Multiply
Next, we will cross-multiply to eliminate the fractions:
(1/3) × 12 - (x/3) × 12 = 7x + 15
This gives us:
4 - 4x = 7x + 15
Step 3: Solve for x
Now, let's solve for x by adding 4x to both sides of the equation:
4 - 4x + 4x = 7x + 15 + 4x 4 = 11x + 15
Subtracting 15 from both sides gives us:
-11 = 11x
Dividing both sides by -11, we get:
x = 1
Conclusion
Therefore, the value of x is 1. We can verify this by plugging x = 1 back into the original equation.
