how many solutions does the equation have -2(6x-4)= -12x

A. one solution*****
B. no solution
C. an infinitive number of solutions
D. impossible to determine

Select all the equations that have one solution

A. 4(2x+2)=8x+9****
B.3x+(-4)=6x-4****
C.9x-9=3(3x-3)****
D. 4x+5x+x=11x-3

Select all the equations that have one solution

A.7x-12=8x=29-x
B.-4+5x=2(3x-4)*****
C.2(3x+5)=6x-19
D.-7=3x+8x=2(6x-4)*****

#1

-2(6x-4)= -12x
-12x + 8 = -12x
8 = 0 which is false, thus NO solution

If you lose your variable and you end up with a FALSE statement, like above, there is no solution
If you lose your variable and you end up with a TRUE statement, there is an infinite number of solutions.

So in #2, I can see that the variables disappear in the first and third, so ....
what do you think?

You also have typos in #2 , 1st and last equations.

To solve the equation -2(6x-4)= -12x, we can follow these steps:

1. Begin by distributing the -2 to both terms inside the parentheses:
-2 * 6x + (-2) * (-4) = -12x
-12x + 8 = -12x

2. Next, combine like terms on both sides of the equation:
-12x + 8 + 12x = -12x + 12x
8 = 0

3. At this point, we can see that the equation leads to an inconsistency. This means there is no solution.
Therefore, the correct option for the number of solutions to the equation -2(6x-4)= -12x is B. no solution.

Now, moving on to selecting the equations that have one solution:

A. 4(2x+2)=8x+9:
Distribute the 4 on the left side:
8x + 8 = 8x + 9
Subtract 8x from both sides:
8 = 9

This equation leads to an inconsistency, so it has no solution. Therefore, it is not an equation with one solution.

B. 3x+(-4)=6x-4:
Combine like terms on both sides:
3x - 4 = 6x - 4
Subtract 3x from both sides:
-4 = 3x - 4
Add 4 to both sides:
0 = 3x

This equation simplifies to 0 = 3x, which means x must be 0. It has one solution.

C. 9x-9=3(3x-3):
Distribute the 3 on the right side:
9x - 9 = 9x - 9
Subtract 9x from both sides:
-9 = -9

This equation is consistent and has infinitely many solutions since any value of x will satisfy it.

D. 4x+5x+x=11x-3:
Combine like terms on both sides:
10x = 11x - 3
Subtract 11x from both sides:
-x = -3
Multiply both sides by -1 (to isolate x):
x = 3

This equation has one solution.

Based on the analysis above, the equations that have one solution are:
B. 3x+(-4)=6x-4
D. 4x+5x+x=11x-3

Therefore, the correct option regarding the equations is B. 3x+(-4)=6x-4 and D. 4x+5x+x=11x-3.