Describe the Number of solutions for the equation. -2(x-1)=2x-2 (1 point)
A. Infinite solution.
B. One solution.
C. No solution.
B
the two lines have different slopes, so they must intersect.
To determine the number of solutions for the equation -2(x-1)=2x-2, we can simplify and solve it step-by-step:
-2(x-1) = 2x-2
Distribute the -2 to the terms inside the parentheses:
-2x + 2 = 2x - 2
Combine like terms by adding 2x to both sides:
-2x + 2x + 2 = 2x - 2 + 2x
The -2x and +2x cancel each other out on the left side of the equation:
2 = 4x - 2
Add 2 to both sides of the equation:
2 + 2 = 4x - 2 + 2
This simplifies to:
4 = 4x
Finally, divide both sides of the equation by 4 to solve for x:
4/4 = 4x/4
1 = x
So, the solution to the equation is x = 1.
Therefore, the answer is B. One solution.
To determine the number of solutions for the equation -2(x-1) = 2x-2, let's simplify it step by step:
-2(x-1) = 2x-2
First, distribute -2:
-2x + 2 = 2x - 2
Next, isolate the x terms on one side by subtracting 2x from both sides:
-4 = 4x - 2
Next, add 2 to both sides:
-2 = 4x
Finally, divide both sides by 4:
-1/2 = x
The equation simplifies to x = -1/2, which means there is only one solution for this equation.
Therefore, the answer is:
B. One solution.