To determine which equation has infinitely many solutions, we can simplify each equation and see if they result in a true statement for all values of \( x \).
A. \( 3x + 5 = 3x - 5 \)
Subtract \( 3x \) from both sides:
\( 5 = -5 \) (False statement)
B. \( 3 - 3x = -3(x - 1) \)
Simplifying the right side:
\( 3 - 3x = -3x + 3 \)
Now, both sides can be simplified further:
\( 3 - 3x = 3 - 3x \) (True statement for all \( x \))
C. \( 3x = 2x + 1 \)
Subtract \( 2x \) from both sides:
\( x = 1 \) (Single solution)
D. \( 4x + 1 = 4(x + 1) \)
Distributing on the right side:
\( 4x + 1 = 4x + 4 \)
Subtract \( 4x \) from both sides:
\( 1 = 4 \) (False statement)
Based on the evaluations, the correct answer is:
B. \( 3 - 3x = -3(x - 1) \) has infinitely many solutions.