Final answer:
The correct answer is option a. To solve the expressions, combine like terms and simplify, resulting in 1/2x - 9 and 1/4x + 2, and then confirm the results are reasonable.
Step-by-step explanation:
To solve the expressions 1/2x + (-7) - 2 and 1/4x - (-2), you should first combine like terms and simplify each expression. For the first expression, combine the constants -7 and -2 to get -9, so the simplified expression is 1/2x - 9. For the second expression, the subtraction of a negative number is the same as addition, so -(-2) becomes +2. This simplifies to 1/4x + 2. After combining like terms, you should check to ensure that the answer is reasonable based on what you know about adding and subtracting negative numbers and positive numbers.
Let's solve the expressions step by step:
For the expression 1/2x + (-7) - 2:
Combine like terms -7 and -2, which gives -9.
Combine the remaining terms 1/2x and -9.
The simplified expression is 1/2x - 9.
For the expression 1/4x - (-2):
Change the double negative -(-2) to a positive 2.
Combine the terms 1/4x and 2.
The simplified expression is 1/4x + 2.