What is the answer to 5p – 9 = 2p + 12
The correct answer and explanation is:
Correct Answer: p=7p = 7
Step-by-Step Explanation:
We are given the equation: 5p−9=2p+125p – 9 = 2p + 12
Our goal is to solve for the variable pp. This is a linear equation, meaning it contains a variable raised only to the first power, and it can be solved using basic algebra.
Step 1: Move all terms with pp to one side
To simplify the equation, we want to get all terms involving pp on one side of the equation and constants on the other. Let’s subtract 2p2p from both sides: 5p−2p−9=2p−2p+125p – 2p – 9 = 2p – 2p + 12 3p−9=123p – 9 = 12
Step 2: Move the constant term to the other side
Now, add 9 to both sides to isolate the term with the variable: 3p−9+9=12+93p – 9 + 9 = 12 + 9 3p=213p = 21
Step 3: Solve for pp
Now, divide both sides by 3 to find the value of pp: 3p3=213\frac{3p}{3} = \frac{21}{3} p=7p = 7
Conclusion:
The solution to the equation 5p−9=2p+125p – 9 = 2p + 12 is p=7\boxed{p = 7}.
This type of algebra problem is common in introductory algebra and helps build foundational problem-solving skills. Solving it involves using inverse operations to isolate the variable step by step. Remember to always perform the same operation on both sides of the equation to keep it balanced. Once the variable is isolated, you can determine its value easily. Checking your solution by plugging it back into the original equation ensures accuracy.