Question

Decide whether 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

Answer 1

1) No solution because 2x-6≠2x
2) Infinite solutions because 3y-9= 3y-9
3) Infinite solutions because 4x- 2= 4x-2
4) One solution

Answer 2

Thank you

Answer 3

1. 2(x - 3) = 2x -- distribute through the parenthesis
2x - 6 = 2x -- add 6 to both sides
2x = 2x + 6 -- subtract 2x from both sides
2x - 2x = 6
0 = 6 (incorrect)
If you answer comes out not equal, then there is no solution

2. 3(y - 3) = 2y - 9 + y -- distribute and combine
3y - 9 = 3y - 9 -- subtract 3y
3y - 3y - 9 = - 9 -- add 9
3y - 3y = -9 + 9
0 = 0 (correct)
If you answer comes out equal, then there is infinite solutions

3. 10x - 2 - 6x = 3x - 2 + x -- combine like terms
4x - 2 = 4x - 2
same thing here...it is gonna come out to 0 = 0 making it have infinite solutions

4. 4(x + 3) + 2x = x - 8
4x + 12 + 2x = x - 8
6x + 12 = x - 8
6x - x = -8 - 12
5x = - 20
x = -4
ONE SOLUTION

Answer 4

Thanks

Answer 5

hi

Answer 6

heyy @sassydiva321

Answer 7

This helped with one of my assignments that I just had LOL

Answer 8

hahaha glad it could help cx @sassydiva321

Answer 9

which one was correct