The Correct Answer and Explanation is:
Correct Answer: 17x
Explanation
The process of simplifying the expression 8x + 9x involves a fundamental algebraic concept known as combining like terms. This method allows us to condense and simplify expressions to make them easier to understand and work with.
In algebra, a “term” is a single mathematical expression. It might be a number, a variable, or a number and variable multiplied together. In the expression 8x + 9x, we have two terms: 8x and 9x. For terms to be considered “like terms,” they must have the exact same variable part, raised to the exact same power. In this case, both terms contain the variable ‘x’ raised to the first power (even though the ‘1’ is not written, x is the same as x¹). Because they share the identical variable part, they are like terms and can be combined.
To combine like terms, you perform the arithmetic operation on their coefficients. The coefficient is the numerical factor that multiplies the variable. For the term 8x, the coefficient is 8. For the term 9x, the coefficient is 9. The expression instructs us to add them.
The steps are as follows:
- Identify the like terms: 8x and 9x.
- Add their coefficients: 8 + 9 = 17.
- Keep the common variable part, which is ‘x’.
- Write the new coefficient with the common variable: 17x.
You can think of this using a simple analogy. If ‘x’ represented an object, such as an apple, the expression 8x + 9x would be like saying “8 apples plus 9 apples.” The logical sum is 17 apples, or 17x. You can add apples to other apples, just as you can combine 8x and 9x. However, you could not simplify 8x + 9y, as that would be like adding 8 apples and 9 oranges; they are not the same kind of object.
Therefore, by combining the like terms, the expression 8x + 9x simplifies completely to 17x.
