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How many solutions does this equation have?

5x+1 = 3x+1
*
none
one
infinite

1 answer

To solve the equation \( 5x + 1 = 3x + 1 \), we can start by isolating \( x \).

  1. Subtract \( 3x \) from both sides: \[ 5x - 3x + 1 = 1 \] This simplifies to: \[ 2x + 1 = 1 \]

  2. Next, subtract 1 from both sides: \[ 2x + 1 - 1 = 1 - 1 \] This simplifies to: \[ 2x = 0 \]

  3. Finally, divide both sides by 2: \[ x = 0 \]

The equation has one solution, which is \( x = 0 \). Therefore, the answer is: one.