The Correct Answer and Explanation is:
Based on the visible portion of the screen, the initial problem involves the expression 1x + y + 6x + 12. The likely first step is to simplify this expression.
Correct Answer:
The simplified form of the expression is 7x + y + 12.
The coefficients in the simplified expression are 7 and 1.
Explanation:
The task is to analyze the algebraic expression 1x + y + 6x + 12. This process typically begins with simplification, which involves combining any “like terms”. Like terms are terms that have the same variable raised to the same power.
First, we identify the like terms within the expression. The terms 1x and 6x are like terms because they both contain the variable x. The term y is distinct, as is the number 12, which is known as a constant.
To simplify, we combine the like terms by adding their coefficients. A coefficient is the numerical part of a term that is multiplied by a variable. For the term 1x, the coefficient is 1. For the term 6x, the coefficient is 6. Adding these coefficients gives us 1 + 6 = 7. This means the combined term for x is 7x.
The other terms, y and 12, do not have any like terms, so they remain as they are. After combining the x terms, we write the new, simplified expression by including all the remaining parts. This gives us the final simplified expression: 7x + y + 12.
Further analysis of this simplified expression allows us to identify its components, which is often a follow up question.
- Terms: The individual parts of the expression separated by addition are 7x, y, and 12.
- Coefficients: As defined, these are the numbers multiplying the variables. The coefficient of x is 7. For the variable y, the coefficient is an implied 1, since y is the same as 1y.
- Variables: The letters representing unknown values are x and y.
- Constant: The term without a variable is the constant. Here, the constant is 12.
