. Select the equation that has infinitely many solutions.(1 point)

Question

Responses

3x=2x+1
3 x is equal to 2 x plus 1

4x+1=4(x+1)
4 x plus 1 is equal to 4 times open paren x plus 1 close paren

3−3x=−3(x−1)
3 minus 3 x is equal to negative 3 times open paren x minus 1 close paren

3x+5=3x−5

Answer 1

To determine which equation has infinitely many solutions, we need to analyze each provided equation:

1. 3x = 2x + 1
   Subtracting 2x from both sides gives us:
   \( 3x - 2x = 1 \)
   \( x = 1 \)
   This has a unique solution.

2. 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. 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.

4. 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).