Final answer:
To simplify the given expression, distribute the multiplication across the parentheses, combine like terms, and then add the constants. The simplified expression results in -11/2n + 43/8.
Step-by-step explanation:
To simplify the expression (1/2)n - (3/4)(8n - (1/2)) + 5, we need to follow the order of operations and combine like terms. First, we'll distribute the (3/4) across the terms in the parentheses:
- (3/4) × 8n = 6n
- (3/4) × (-1/2) = -3/8
The expression now looks like this:
(1/2)n - 6n + 3/8 + 5
Next, we combine like terms, which are the 'n' terms:
(1/2)n - 6n = -11/2n
We can add the constants, 3/8 and 5, remembering that 5 is equivalent to 40/8:
3/8 + 40/8 = 43/8
The simplified expression is:
-11/2n + 43/8
From here, we can check our answer to make sure it's reasonable and confirm that we've eliminated terms wherever possible.