Consider the equation $3 p-7+p=13$. What is the resulting equation after the first step in the solution?
A. $p-7=13-3 p$
B. $2 p-7=13$
C. $3 p-7=13-p$
D. $4 p-7=13
Answer (1)
Combine like terms: 3 p + p = 4 p .
Substitute the combined term back into the equation: 4 p − 7 = 13 .
The resulting equation is 4 p − 7 = 13 .
The equation after the first step is 4 p − 7 = 13 .
Explanation
Understanding the Equation We are given the equation 3 p − 7 + p = 13 . Our goal is to simplify this equation by combining like terms.
Combining Like Terms We need to combine the terms with the variable p . We have 3 p and + p on the left side of the equation. Adding these terms together, we get 3 p + p = 4 p .
Simplified Equation Now, we substitute 4 p back into the original equation, replacing 3 p + p . This gives us the simplified equation 4 p − 7 = 13 .
Final Result Therefore, the resulting equation after the first step in the solution is 4 p − 7 = 13 .
Examples
Imagine you're balancing a checkbook. You have several entries with the same variable (like expenses 'x'). Combining these like terms simplifies the equation, making it easier to solve for the unknown variable, helping you determine your overall balance. This principle of combining like terms is fundamental in algebra and is used in various real-life scenarios, such as calculating total costs, determining distances, and solving for unknown quantities in physics or engineering problems.
