Which equation has infinitely many solutions?
Responses
A 9x − 3 = 3x + 6x + 2 + 39x − 3 = 3x + 6x + 2 + 3
B 12(x + 8) = 11x − 512(x + 8) = 11x − 5
C 11x − 2x + 15 = 8 + 7 + 9x11x − 2x + 15 = 8 + 7 + 9x
D 5x − 8 = 11 − 7x + 12x
In order for an equation to have infinitely many solutions, the equation must be an identity, meaning that both sides of the equation are equal for all values of x.
Looking at the given options:
A) 9x - 3 = 3x + 6x + 2 + 39x - 3 = 3x + 6x + 2 + 3
This equation can be simplified to 9x - 3 = 48x - 3, which is not true for all values of x. Therefore, option A is not the correct answer.
B) 12(x + 8) = 11x - 5
This equation can be simplified to 12x + 96 = 11x - 5. Simplifying further, we get x = -101. This equation does not hold true for all values of x. Therefore, option B is not the correct answer.
C) 11x - 2x + 15 = 8 + 7 + 9x11x - 2x + 15 = 8 + 7 + 9x
This equation can be simplified to 9x + 15 = 24 + 9x. Simplifying further, we get 15 = 24, which is not true for any value of x. Therefore, option C is not the correct answer.
D) 5x - 8 = 11 - 7x + 12x
This equation can be simplified to -7x + 12x + 5x = 11 + 8, which simplifies to 10x = 19. This equation is true for all values of x. Therefore, option D is the correct answer.
Therefore, the equation that has infinitely many solutions is option D) 5x - 8 = 11 - 7x + 12x.