Can someone help me answer this question? I need to Combine the like terms. My teacher said I got a portion incorrect.

Question~~ – ½ a + ¾ b – (a – 8b)
My answer~~
-1/2a+1a
1/2a
3/4b+8b
(3/4+8)b
8 3/4b
The answer is 1/2a+8 3/4

should have been -1/2a - a and you also dropped the b in 8 3/4b

I am not crazy about the solution done in parts.
Better form would be

– ½ a + ¾ b – (a – 8b)
= -1/2a + 3/4b - a + 8b
= -1/2a - a + 8b + 3/4b
= -3/2a + 35/4b
or
= -1 1/2a + 8 3/4b

Ok thanks so much!!

To combine like terms, we need to add or subtract terms with the same variable and exponent. Let's break down the given expression:

– ½ a + ¾ b – (a – 8b)

First, distribute the negative sign inside the parentheses:

– ½ a + ¾ b – a + 8b

Now, let's arrange the terms in a simplified form:

(– ½ a – a) + (¾ b + 8b)

Combine the terms with "a" by adding the coefficients:

(– ½ - 1) a + (¾ + 8) b

Simplify further:

-1 ½ a + 8 ¾ b

Now we have the correctly combined like terms: -1 ½ a + 8 ¾ b

Based on your result, it appears that there was an error in the step where you combined the coefficients. Instead of adding -1/2 and 1, you mistakenly subtracted them. The correct answer should be -1 ½ a + 8 ¾ b, not 1/2a + 8 3/4.