The Correct Answer and Explanation is:
Correct Answer: p = 9
The problem presented is a simple linear equation, p – 9 = 0. The objective when solving such an equation is to determine the value of the unknown variable, which is p in this instance. The core principle for solving this is to isolate the variable on one side of the equals sign. To do this, we employ the concept of inverse operations and the property of equality, which dictates that whatever action we take on one side of the equation, we must also perform on the other side to maintain the balance.
In the given equation, the variable p has 9 subtracted from it. The inverse operation of subtraction is addition. Therefore, to cancel out the -9 on the left side and isolate p, we need to add 9. According to the property of equality, if we add 9 to the left side, we must also add 9 to the right side.
Here is the step by step process:
- Start with the original equation:
p – 9 = 0 - Add 9 to both sides of the equation to isolate p:
p – 9 + 9 = 0 + 9 - Simplify both sides. On the left, -9 and +9 cancel each other out, leaving only p. On the right, 0 + 9 equals 9.
p = 9
This gives us our final answer. We can verify this solution by substituting the value of p back into the original equation. If p = 9, then the equation becomes 9 – 9 = 0. Since this simplifies to 0 = 0, which is a true statement, our solution is confirmed to be correct. The value that makes the equation true is 9.
