Step 1: Understand the Equation
To solve the equation 2/3x - 1/12 = 3/2x, we need to isolate the variable x.
Step 2: Eliminate Fractions
To make calculations easier, we can eliminate fractions by finding a common denominator. The denominators here are 3, 12, and 2. The least common multiple of these numbers is 12.
Step 3: Multiply Through by 12
Multiply each term in the equation by 12 to eliminate the fractions:
- (12 * 2/3)x - (12 * 1/12) = (12 * 3/2)x
This simplifies to:
- 8x - 1 = 18x
Step 4: Rearranging the Equation
Next, we will get all terms involving x on one side and constant terms on the other:
- 8x - 18x = 1
This simplifies to:
-10x = 1
Step 5: Solve for x
Now, divide both sides by -10 to isolate x:
- x = 1 / -10
This gives us:
- x = -1/10
Conclusion
The solution to the equation 2/3x - 1/12 = 3/2x is:
- x = -1/10
By following these steps, we have effectively solved the equation while ensuring clarity in each stage of the process.