The Correct Answer and Explanation is:
The correct answer is 40x + 4.
To arrive at this answer, we must simplify the original algebraic expression shown in the image, which is 40x + 43 – 39. The process of simplification in algebra involves combining “like terms.” Like terms are terms that have the same variable part raised to the same power. Constant numbers, which are numbers without variables, are also considered like terms with each other.
Let’s analyze the components of the given expression:
- 40x: This is a variable term. It consists of a coefficient, which is 40, and a variable, which is ‘x’.
- +43: This is a constant term. It is a fixed numerical value.
- -39: This is another constant term.
The first step in simplifying is to identify the like terms. In this expression, the constant terms +43 and -39 are like terms. The variable term 40x is the only term with the variable ‘x’, so it has no other like terms to combine with. Therefore, the 40x part of the expression will remain unchanged throughout the simplification process.
The next step is to combine the like terms by performing the indicated mathematical operation. Here, we need to subtract 39 from 43.
The calculation is:
43 – 39 = 4
Now that we have combined the constant terms into a single value, we can rewrite the entire expression in its simplified form. We take the variable term, 40x, and add the result of our calculation for the constants, which is +4.
This gives us the final, simplified expression: 40x + 4.
This expression cannot be simplified any further because 40x and 4 are not like terms. One term’s value depends on the variable ‘x’, while the other is a fixed constant. They cannot be merged into a single term, making 40x + 4 the simplest form of the original expression.
