To determine which equation has infinitely many solutions, we need to analyze each provided equation:
-
3x = 2x + 1
Subtracting 2x from both sides gives us:
\( 3x - 2x = 1 \)
\( x = 1 \)
This has a unique solution. -
4x + 1 = 4(x + 1)
Expanding the right side gives:
\( 4x + 1 = 4x + 4 \)
Subtracting \( 4x \) from both sides:
\( 1 = 4 \)
This is a contradiction, meaning there are no solutions. -
3 - 3x = -3(x - 1)
Expanding the right side gives:
\( 3 - 3x = -3x + 3 \)
Adding \( 3x \) to both sides:
\( 3 = 3 \)
This is true for all x, which means there are infinitely many solutions. -
3x + 5 = 3x - 5
Subtracting \( 3x \) from both sides gives:
\( 5 = -5 \)
This is a contradiction, meaning there are no solutions.
The equation with infinitely many solutions is:
3 - 3x = -3(x - 1).