To determine which equation has infinitely many solutions, we need to find the equation where the variables cancel out and we are left with a true statement.
Let's analyze each of the given equations:
A) 9x - 3 = 3x + 6x + 2 + 39x - 3 = 3x + 6x + 2 + 3
Combining like terms, we have:
9x - 3 = 8x + 5
Subtracting 8x from both sides, we get:
x - 3 = 5
Adding 3 to both sides gives:
x = 8
This equation has a single solution, so it does not have infinitely many solutions.
B) 12(x + 8) = 11x - 5
Expanding the brackets, we have:
12x + 96 = 11x - 5
Subtracting 11x from both sides, we find:
x + 96 = -5
Subtracting 96 from both sides, we get:
x = -101
This equation has a single solution, so it does not have infinitely many solutions.
C) 11x - 2x + 15 = 8 + 7 + 9x
Combining like terms, we have:
9x + 15 = 15 + 9x
Subtracting 9x from both sides, we obtain:
15 = 15
This equation simplifies to 15 = 15, which is true for any value of x. Therefore, this equation has infinitely many solutions.
D) 5x - 8 = 11 - 7x + 12x
Combining like terms, we have:
5x - 8 = 11 + 5x
Subtracting 5x from both sides, we find:
-8 = 11
This equation simplifies to -8 = 11, which is false. Therefore, this equation does not have any solutions.
In conclusion, the equation C) 11x - 2x + 15 = 8 + 7 + 9x has infinitely many solutions.
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