Answer:
C) x + 9 = x + 9
Explanation:
An equation has infinite solutions if can simplify to the format: a = a, where a is any number.
This is because it means that any value you plug into x will give you the same true equation and answer.
C meets these requirements as it is already in format a=a, but if we further simplify it, we can see how it works:
Subtract x from both sides: 9=9
Subtract 9 from both sides: x=x
Subtract (x+9) from both sides: 0=0
We can see that C has infinite solutions because any value you put in for x, it will cancel itself out when you solve it, therefore it has infinite solutions.
E.g. x=5
(5) + 9 = (5) + 9
14 = 14
E.g. x=-25
(-25) + 9 = (-25) = 9
-16 = -16
We can also answer this question by solving all the other equations:
A) 2x + 5 - 2x = 2x - 2x + 8
5 = 8
This is not true so this equation has NO solutions.
B) 5x - 2x - 1 = 2x - 2x + 4
3x - 1 + 1 = 4 + 1
3x = 5
x = 5/3 (One solution)
D) I think you've missed a sign here, but it is solvable either way to get to one solution.
Hope this helped!