To determine which equation has infinitely many solutions, we need to look for an equation that simplifies to a true statement for all values of \(x\).
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Equation: \(3x = 2x + 1\)
Solving for \(x\):
\[3x - 2x = 1\]
\[x = 1\]
This has a single solution. -
Equation: \(3x + 5 = 3x - 5\)
Solving for \(x\):
\[3x + 5 - 3x = -5\]
\[5 = -5\]
This is false and has no solutions. -
Equation: \(4x + 1 = 4(x + 1)\)
Expanding the right-hand side:
\[4x + 1 = 4x + 4\]
\[1 = 4\]
This is false and has no solutions. -
Equation: \(3 - 3x = -3(x - 1)\)
Expanding the right-hand side:
\[3 - 3x = -3x + 3\]
\[3 - 3x + 3x = 3\]
\[3 = 3\]
This is a true statement for all values of \(x\), meaning it has infinitely many solutions.
Therefore, the equation that has infinitely many solutions is:
\(3 - 3x = -3(x - 1)\).