Consider the equation 7x − 6 + 3 = 5x + 2x + 5
Which equation has infinitely many solutions?
Responses
A 9x − 3 = 3x + 6x + 2 + 3
B 12(x + 8) = 11x − 5
C 11x − 2x + 15 = 8 + 7 + 9x
D 5x − 8 = 11 − 7x + 12x
The equation that has infinitely many solutions is the one that simplifies to always be true. This means that the equation is true for any value of x.
Analyzing the given options:
A: 9x − 3 = 3x + 6x + 2 + 3
Simplifying the equation, we get:
9x - 3 = 9x + 5
This equation is not always true, so it does not have infinitely many solutions.
B: 12(x + 8) = 11x − 5
Expanding the equation and simplifying, we get:
12x + 96 = 11x - 5
This equation is inconsistent and does not have a unique solution, so it does not have infinitely many solutions.
C: 11x − 2x + 15 = 8 + 7 + 9x
Simplifying the equation, we get:
9x + 15 = 15 + 9x
This equation is always true, which means it has infinitely many solutions.
D: 5x − 8 = 11 − 7x + 12x
Simplifying the equation, we get:
-9x - 8 = 11
This equation is inconsistent and does not have a unique solution, so it does not have infinitely many solutions.
Therefore, the equation that has infinitely many solutions is option C: 11x − 2x + 15 = 8 + 7 + 9x.