The correct answer and explanation is:
Correct Answer:
-8x – 12
Explanation:
The problem requires us to simplify the expression (2x – 7) + (-10x – 5). To do this, we need to combine the like terms. Like terms are terms that contain the same variable raised to the same power. In this expression, the terms with the variable x are like terms, and the constant numbers are also like terms.
First, we can remove the parentheses. Since the operation connecting the two binomials is addition, we can remove the parentheses without changing the signs of the terms inside. The expression can be rewritten as:
2x – 7 – 10x – 5
Next, we identify and group the like terms to make simplification easier. The terms containing x are 2x and -10x. The constant terms are -7 and -5. We can rearrange the expression to place these like terms next to each other, a step permitted by the commutative property of addition.
(2x – 10x) + (-7 – 5)
Now, we perform the arithmetic for each group of like terms.
For the variable terms, we combine the coefficients (the numbers in front of the x). We calculate 2 – 10, which equals -8. This gives us a single term, -8x.
For the constant terms, we combine -7 and -5. When we subtract 5 from negative 7, or add the two negative numbers together, we get -12.
Finally, we combine these simplified parts to form the final expression. By putting the results from the previous step together, we get -8x – 12. This expression is in its simplest form because the remaining terms, -8x and -12, are not like terms and cannot be combined any further.
