Step 1: Simplify the Equation
To solve the equation \(0.2(2x-1) - 0.5(3x-1) = 0.4\), first, let's distribute the constants in the parentheses.
- \(0.2(2x) - 0.2(1) - 0.5(3x) + 0.5(1) = 0.4\)
This simplifies to:
- \(0.4x - 0.2 - 1.5x + 0.5 = 0.4\)
Step 2: Combine Like Terms
Now, combine the \(x\) terms and the constant terms.
- Combine \(0.4x - 1.5x\):
- \(0.4x - 1.5x = -1.1x\)
- Combine \(-0.2 + 0.5\):
- \(-0.2 + 0.5 = 0.3\)
So, the equation now reads:
- \(-1.1x + 0.3 = 0.4\)
Step 3: Isolate \(x\)
Next, we want to isolate \(x\):
- Subtract \(0.3\) from both sides:
- \(-1.1x = 0.4 - 0.3\)
- \(-1.1x = 0.1\)
Now, divide by \(-1.1\):
- \(x = \frac{0.1}{-1.1} = -\frac{1}{11}\)
Step 4: Conclusion
The solution to the equation \(0.2(2x-1) - 0.5(3x-1) = 0.4\) is:
- \(x = -\frac{1}{11}\)
This value of \(x\) satisfies the original equation.