Question

Decide whether each equation has one, no solutions, or infanatly many solutions

1.) 2(x - 3) = 2x

One solution
no solutions
many solutions
infinatly many solutions

2.) 3(y - 3?) = 2y - 9 + y

One solution
no solutions
many solutions
infinatly many solutions

3.)10x - 2 - 6x = 3x -2 + x

One solution
no solutions
infinatly many solutions

4.) 4(x + 3) + 2x = x - 8

One solution
no solutions
infinatly many solutions

MY ANSWERS

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

Answer 1

1. Actually it's B.
Expanding,
2(x - 3) = 2x
2x - 6 = 2x
-6 = 0
Note that if you get an answer like this (constant = zero), there is no solution.

2. It's D. (btw I don't know why you put question mark beside 3)
Expanding,
3(y - 3) = 2y - 9 + y
3y - 9 = 3y - 9
or
0 = 0
Note that if you get an answer like this (zero = zero), there are infinite solutions.

3. It's C.
Expanding,
10x - 2 - 6x = 3x -2 + x
4x - 2 = 4x - 2
0 = 0
(infinite solutions)

4. It's A.
Expanding,
4(x + 3) + 2x = x - 8
4x + 12 + 2x = x - 8
6x + 12 = x - 8
5x = -20
x = -4
(one solution)

I guess you have to study these topics.
Hope this helps :3

Answer 2

Check your answers again.

1. -3 = 0?

2. 3y-9 = 3y -9 (identity)

3. 4x-2 = 4x-2 (identity)

4. 6x+12 = x-8

5x = -20

Answer 3

Thank you Jai, I understand it all perfectly now.

Answer 4

7x+3=7x+b

Answer 5

1)B
2)C
3)C
4)A

For the students that do not have 4 options for answers.