Solve the Equation: 3/4(1/6x-1/3)=3x-11/2
In this article, we will solve the equation 3/4(1/6x-1/3)=3x-11/2. This equation involves fractions and variables, making it a challenging problem to solve. However, with the right steps and techniques, we can find the solution.
Step 1: Simplify the Left Side of the Equation
To begin with, let's simplify the left side of the equation:
3/4(1/6x-1/3)
To simplify this expression, we need to follow the order of operations (PEMDAS):
- Multiply 3/4 by 1/6x: 3/4 × 1/6x = 1/8x
- Multiply 3/4 by -1/3: 3/4 × -1/3 = -1/4
- Combine the two results: 1/8x - 1/4
So, the left side of the equation becomes:
1/8x - 1/4 = 3x - 11/2
Step 2: Equate the Expressions
Now, we have a simplified equation:
1/8x - 1/4 = 3x - 11/2
Our goal is to equate the expressions on both sides of the equation.
Step 3: Add 1/4 to Both Sides
To get rid of the negative term, let's add 1/4 to both sides of the equation:
1/8x = 3x - 11/2 + 1/4
Step 4: Simplify the Right Side
Simplify the right side of the equation:
3x - 11/2 + 1/4 = 3x - 21/4 + 1/4 = 3x - 20/4
Step 5: Equate the Expressions Again
Now, we have:
1/8x = 3x - 20/4
Step 6: Solve for x
To solve for x, we can multiply both sides of the equation by 8 to eliminate the fraction on the left side:
x = 24x - 40
Step 7: Solve the Linear Equation
Now, we have a simple linear equation:
24x - x = 40
Subtract 24x from both sides:
-23x = 40
Divide both sides by -23:
x = -40/23
Therefore, the solution to the equation 3/4(1/6x-1/3)=3x-11/2 is x = -40/23.
