Final answer:
The simplified equation '4x + 8 = 4x + 8' shows that there are infinite solutions to the equation, as every value for 'x' will yield a true statement after simplification.
Step-by-step explanation:
The given question is about simplifying a mathematical equation to determine its solution. The best description of the solution, after simplifying the expressions on each side of the equal sign, depends on comparing the two sides after simplification. For example, if we compare the given options logically:
- A: No solution is correct if the two sides of the equation after simplification do not equal each other, and no value of 'x' will satisfy the equation.
- B: One solution is correct if the equation simplifies to an impossible statement like 12 = 52 which cannot be true for any value of 'x'.
- C: One solution is correct if the equation can be simplified further to find a specific numerical value for 'x'.
- D: Infinite solutions are correct if, after simplification, we have an identity where both sides of the equation are identical, which means any value for 'x' will satisfy the equation.
In this case, option D, the simplified equation reads 4x + 8 = 4x + 8. This indicates that every value of 'x' will satisfy the equation since subtracting '4x' from both sides leaves us with 8 = 8, which is always true. Therefore, there are infinite solutions to this equation.