Which of the following equations has an infinite number of solutions?

A. 3x-3=-4x
B. 2y+4-y=16
C. 7x+5=4x+5+3x
D. 6y-2=2(y-1)***
Is the answer D?

Yes, the answer is D. The equation 6y - 2 = 2(y - 1) has an infinite number of solutions.

To determine this, we can simplify each equation and observe the relationships between the variables.

A. 3x - 3 = -4x
By combining like terms, we get 7x = 3. Dividing both sides by 7 gives x = 3/7. This equation has a specific solution, not an infinite number of solutions.

B. 2y + 4 - y = 16
Simplifying, we have y + 4 = 16. Subtracting 4 from both sides, we get y = 12. This equation also has a specific solution, not an infinite number of solutions.

C. 7x + 5 = 4x + 5 + 3x
By combining like terms, we get 7x + 5 = 7x + 5. Subtracting 7x and 5 from both sides results in 0 = 0. This equation is always true for any value of x, but it does not have an infinite number of solutions since all values of x satisfy it.

D. 6y - 2 = 2(y - 1)
Expanding the expression inside the parentheses, we have 6y - 2 = 2y - 2. By subtracting 2y from both sides, the equation becomes 4y - 2 = -2. Adding 2 to both sides yields 4y = 0. Then we can divide both sides by 4 to get y = 0. This equation has an infinite number of solutions because any value of y can satisfy it.

Therefore, the correct answer is D.

Lets evaluate D

6y-2=2(y-1)
Now distribute the 2

6y-2=2y-2
Add two to both sides....in this case they cancel each other.

Now we have 6y=2y
The only number that will make this equal is 0. SO y=0 here.

So D cant be the answer.

Ok B then?