Decide whether the each equation has one solution, no solutions,or infinitely many solutions.

1. 2(x-3)= 2X
A.One solution
B.No solutions
C.Infinitely many solutions

2. 3(y-3)= 2y-9+y
A.One solution
B.No solutions
C.Infinitely many solutions

3. 10x-2-6x = 3x-2+x
A.One solution
B.No solutions
C.Infinitely many solutions

4. 4(x+3)+2x=x-8
A.One solution
B.No solutions
C.Infinitely many solutions

My answers:
1.B
2.A
3.C
4.C

6 answers

My answers:

1. B
2. C
3. C
4. A

Thanks, Steve. You were right.

Steve is right..thanks!!

Omg thx so much <3 xoxoxo

its been 7 years and the answears are the same xD L's in the chat ladies and gentlemen

To determine whether each equation has one solution, no solutions, or infinitely many solutions, we can simplify the equations and analyze the results. Here's how to get the answer for each equation:

1. 2(x-3) = 2x
First, distribute the 2 to both terms inside the parentheses:
2x - 6 = 2x
By subtracting 2x from both sides, we get:
-6 = 0

Since -6 is not equal to 0, this equation is contradictory, indicating that there are no solutions.
Therefore, the answer is B. No solutions.

2. 3(y-3) = 2y-9+y
First, distribute the 3 to both terms inside the parentheses:
3y - 9 = 2y - 9 + y
Combine like terms on the right side:
3y - 9 = 3y - 9
By subtracting 3y from both sides, we get:
-9 = -9

Since -9 is equal to -9, this equation is an identity, implying infinitely many solutions.
Therefore, the answer is C. Infinitely many solutions.

3. 10x-2-6x = 3x-2+x
Combine like terms on both sides:
4x - 2 = 4x - 2
By subtracting 4x from both sides, we get:
-2 = -2

Since -2 is equal to -2, this equation is an identity, implying infinitely many solutions.
Therefore, the answer is C. Infinitely many solutions.

4. 4(x+3) + 2x = x-8
First, distribute the 4 to both terms inside the parentheses:
4x + 12 + 2x = x - 8
Combine like terms on both sides:
6x + 12 = x - 8
By subtracting x and 12 from both sides, we get:
5x = -20
Divide by 5:
x = -4

Since x is a specific numerical value, this equation has one solution.
Therefore, the answer is A. One solution.