Final answer:
After simplifying the equation and attempting to isolate x, we find a contradiction which suggests the equation -2(-3x+1) = -(-6x+3) has no solution, as the lines are parallel and do not intersect.
Step-by-step explanation:
To find the value of x in the equation -2(-3x+1) = -(-6x+3), we first simplify both sides by distributing the negative signs through the parentheses:
- Multiply -2 by both -3x and +1 to get the left side of the equation: 6x - 2.
- Multiply -1 by both -6x and +3 to get the right side of the equation: 6x - 3.
Now, our equation looks like this: 6x - 2 = 6x - 3. Next, we attempt to isolate x on one side:
- Subtract 6x from both sides: This step leads to 0 = -1, which indicates there is a contradiction.
- Since there is no x term remaining, this means our original equation has no solution. The lines represented by these equations are parallel and will never intersect.