Question 33

Infinitely many

The equation 3x + 9 = 3x - 12 has infinitely many solutions. This occurs because, when simplifying the equation, both sides are equivalent, indicating that any value of x satisfies the equation.

A) 1

Option A is incorrect because the equation does not simplify to a single solution; rather, it simplifies to an identity that holds for all values of x.

B) 2

Option B is also incorrect since there are not just two distinct solutions to the equation. The simplification shows that the equation is true for every value of x, not limited to two.

C) 3

Option C is incorrect as well. The equation does not yield a specific number of solutions such as three; instead, it reveals that every value of x is a solution.

D) Infinitely many

Option D correctly states that there are infinitely many solutions to the equation. This is evident from the fact that both sides of the equation simplify to the same expression, demonstrating that any value of x will satisfy the equation.

Conclusion

The correct answer is that the equation has infinitely many solutions because it simplifies to an identity. All other options fail to recognize that the left and right sides of the equation are equivalent, which leads to the conclusion that every value of x is a solution. Thus, the only accurate choice is that there are infinitely many solutions.