The equation provided is:

$-2(x - 3) + 4x = -(-x + 1)$

Step 1: Expand and simplify both sides

• Expand $-2(x - 3)$: $-2(x - 3) = -2x + 6$
• Expand $-(-x + 1)$: $-(-x + 1) = x - 1$

Substitute back into the equation: $(-2x + 6) + 4x = x - 1$

Step 2: Combine like terms

Simplify the left-hand side: $-2x + 4x + 6 = 2x + 6$

The equation becomes: $2x + 6 = x - 1$

Step 3: Isolate $x$

• Subtract $x$ from both sides: $2x - x + 6 = -1$ $x + 6 = -1$

• Subtract 6 from both sides: $x = -1 - 6$ $x = -7$

Final Answer:

$x = -7$

Would you like further clarification or details?

Relative Questions:

1. What steps can be added to explain why distributing signs is crucial in this problem?
2. How can you verify the solution by substituting $x = -7$ back into the original equation?
3. What happens if the equation has variables on both sides and no solution?
4. How does this method compare to graphing the equation?
5. Are there other methods, like substitution, that could simplify solving this equation?

Tip:

Always simplify expressions fully before moving terms across the equals sign to avoid errors!