Step 1: Set Up the Equation
To solve the equation:
x - (x - 1)/2 = 1 - (x - 2)/3
we'll first eliminate the fractions by finding a common denominator.
Step 2: Find Common Denominator
The common denominator for 2 and 3 is 6. We will multiply every term by 6:
- 6 * x
- 6 * (x - 1)/2
- 6 * 1
- 6 * (x - 2)/3
This results in:
6x - 3(x - 1) = 6 - 2(x - 2)
Step 3: Distribute Terms
Now, distribute the terms:
- Left Side: 6x - 3x + 3
- Right Side: 6 - 2x + 4
So, the equation simplifies to:
3x + 3 = 10 - 2x
Step 4: Combine Like Terms
Next, we will move all x terms to one side and constant terms to the other side:
3x + 2x = 10 - 3
This gives us:
5x = 7
Step 5: Solve for x
Now, divide both sides by 5:
x = 7/5
Step 6: Final Answer
Thus, the solution for x is:
x = 1.4
Conclusion
To summarize, we solved the equation step-by-step, starting from eliminating fractions to isolating x. The final answer is x = 1.4.