How many solutions does the equation 3x + 9 = 3x - 12 have?

Rationale

The equation 3x + 9 = 3x - 12 has 0 solutions.

When we simplify the equation, we can see that the terms involving x cancel out, leading to a contradiction. This indicates that there are no values of x that can satisfy the equation.

A (0) CORRECT

This is correct because, upon simplifying the equation, we find that it reduces to 9 = -12, which is a false statement. Therefore, there are no solutions to this equation.

B (1) YOUR ANSWER

This option suggests that there is one solution to the equation. However, since the simplification leads to a contradiction, it cannot have a single solution. There are no values of x that will satisfy the equation.

C (2) YOUR ANSWER

This choice indicates that there are two solutions. Given that the equation simplifies to an impossible statement (9 = -12), this option is incorrect as well. A linear equation can only have either one solution or none at all.

D (3) YOUR ANSWER

Proposing three solutions is also incorrect. Similar to the previous choices, the simplification of the equation demonstrates that it does not hold true, hence there are no solutions available.

E (Infinitely many) YOUR ANSWER

This option implies that there are infinite solutions to the equation. However, since the original equation results in a contradiction, it cannot possess infinitely many solutions.

Conclusion

The equation 3x + 9 = 3x - 12 simplifies to a false statement, confirming that there are no solutions available. All other options incorrectly suggest the existence of one or more solutions, which does not apply in this case.