Select the equation that has infinitely many solutions.

Question

A. 3x + 5 = 3x - 5
B. 3 - 3x = -3(x - 1)
C. 4x + 1 = 4(x + 1)
D. 3x = 2x + 1

Answer 1

To determine which equation has infinitely many solutions, we need to simplify each equation and see if they lead to a true statement regardless of the value of \( x \) (indicating infinitely many solutions).

Option A: \( 3x + 5 = 3x - 5 \)
Subtract \( 3x \) from both sides:
\( 5 = -5 \)
This is a false statement, so there are no solutions.

Option B: \( 3 - 3x = -3(x - 1) \)
Distribute on the right side:
\( 3 - 3x = -3x + 3 \)
Add \( 3x \) to both sides:
\( 3 = 3 \)
This is a true statement, so there are infinitely many solutions.

Option C: \( 4x + 1 = 4(x + 1) \)
Distribute on the right side:
\( 4x + 1 = 4x + 4 \)
Subtract \( 4x \) from both sides:
\( 1 = 4 \)
This is a false statement, so there are no solutions.

Option D: \( 3x = 2x + 1 \)
Subtract \( 2x \) from both sides:
\( x = 1 \)
This has a single solution.

Therefore, the equation that has infinitely many solutions is Option B: \( 3 - 3x = -3(x - 1) \).

Answer 2

are you sure this is correct

Answer 3

Let's double-check the analysis of each equation to ensure accuracy:

Option A: \( 3x + 5 = 3x - 5 \)

Subtract \( 3x \) from both sides: \[ 5 = -5 \] This statement is false, so there are no solutions.

Option B: \( 3 - 3x = -3(x - 1) \)

Start by distributing on the right side: \[ 3 - 3x = -3x + 3 \] Now add \( 3x \) to both sides: \[ 3 = 3 \] This is a true statement and implies that the equation holds for any \( x \), which means there are infinitely many solutions.

Option C: \( 4x + 1 = 4(x + 1) \)

Distribute on the right-hand side: \[ 4x + 1 = 4x + 4 \] Subtract \( 4x \) from both sides: \[ 1 = 4 \] This statement is false, so there are no solutions.

Option D: \( 3x = 2x + 1 \)

Subtract \( 2x \) from both sides: \[ x = 1 \] This equation has a single solution.

Conclusion

After reviewing all the options again, it is confirmed that:

• Option B is indeed the correct answer as it represents an identity (true for all \( x \)), and thus it has infinitely many solutions.

Thank you for the opportunity to clarify! If you have any further questions, feel free to ask.