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Which of the following equations has infinitely many solutions?

A) 3x - 5 = -5 + 3x
B) 2x + 3 = 5 + 3x
C) 2x + 3 = 5 + 2x
D) 3x - 5 = -5 + 2x

1 Answer

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Final answer:

The equation that has infinitely many solutions from the choices provided is A) 3x - 5 = -5 + 3x, as the expression is identical on both sides once simplified, indicating the equation is valid for any value of x.

Step-by-step explanation:

The equation that has infinitely many solutions is A) 3x - 5 = -5 + 3x. In this equation, both sides are identical once simplified, meaning this equation is true for any value of x. Infinitely many solutions occur when the equation represents the same line in a graph; in this case, both sides of the equation simplify to 3x - 5, indicating the same line.

Hence, any value of x will satisfy the equation.

To establish that A is the correct answer, we can rearrange the equation as follows:

  • Add 5 to each side: 3x - 5 + 5 = -5 + 5 + 3x
  • Simplify both sides: 3x = 3x
  • The equation simplifies to a statement that's always true, indicating infinitely many solutions.

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