Final answer:
By simplifying the equation 5x + 7 = 3x - 5, it is clear that it has a single solution, x = -6, and not infinitely many solutions.
Step-by-step explanation:
The question whether the equation 5x + 7 = 3x - 5 has infinitely many solutions can be tackled by simplifying and solving the equation. To do this, we apply the principle of eliminating terms.
- Subtract 3x from both sides to get 2x + 7 = -5.
- Now subtract 7 from both sides to get 2x = -12.
- Divide both sides by 2 to find x, which gives us x = -6.
This process shows us that the equation has a single solution, x = -6, not infinitely many solutions. We can check our answer to confirm that it makes both sides of the original equation equal when x is substituted back into the equation.