Final Answer:
The solution to the equation 2.5(2p + 5) = 5p + 12.5 is p = 2.
Step-by-step explanation:
To solve the equation, start by distributing the 2.5 on the left side of the equation to both terms within the parentheses: 5p + 12.5 = 5p + 12.5. This results in the simplified equation 5p + 12.5 = 5p + 12.5, implying that the variable term 5p is the same on both sides. Therefore, any value of p satisfies the equation. The solution is thus any real number, and in this case, the simplest solution is p = 2.
It's important to note that when an equation simplifies to a true statement (like 0 = 0 or 5p = 5p), the solution is all real numbers. However, if the equation simplifies to a false statement (like 0 = 1), there is no solution. In this case, since the equation simplifies to a true statement, p can take any real value. The choice of p = 2 is a specific solution among many possible solutions to the equation.
In summary, the solution to the equation 2.5(2p + 5) = 5p + 12.5 is p = 2, and this solution is supported by the algebraic simplification that shows both sides of the equation are equal for any value of p.