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.