Question 24

Infinitely many

The equation 3x + 9 = 3x - 12 simplifies to a situation where both sides of the equation are identical when manipulated, indicating that there are infinitely many solutions.

A) 1

This option is incorrect because the equation does not simplify to a single solution. Instead, the manipulation shows that the two sides of the equation are equivalent, resulting in an infinite number of solutions.

B) 2

This option is also incorrect as the equation does not yield two distinct solutions. The simplification reveals that it results in a tautology, not two separate answers.

C) 3

This choice is incorrect because the equation does not produce three solutions. The analysis indicates that the equation leads to an identity rather than a scenario with multiple distinct solutions.

D) Infinitely many

This option is correct as the equation simplifies to an identity, meaning that any value of x will satisfy the equation, thereby resulting in infinitely many solutions.

Conclusion

The correct answer is that there are infinitely many solutions to the equation, as it simplifies to a true statement for all values of x. All other options fail because they suggest a finite number of solutions, which is inconsistent with the nature of the equation.