9(k+1/3)+10(1/2k−1)
You interpreted 10(1/2k−1) as 10(1/(2k) -1) = 5/k - 10
I'm pretty sure they meant
9(k+1/3)+10(1/2 k−1) = 9k+3+5k-10 = 14k-7
Apologies for the incorrect interpretation. You are right.
9(k+1/3) + 10(1/2k-1)
= 9k + 3 + 10(1/2k) - 10
= 9k + 3 + 5k - 10
= 14k - 7
To simplify the expression 9(k+1/3) + 10(1/2k-1), we should follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
Step 1: Simplify within parentheses:
9(k+1/3) = 9k + 9(1/3) = 9k + 3.
And 10(1/2k-1) = 10/2k -10(1) = 5k - 10.
Now the expression becomes:
9k + 3 + 5k - 10.
Step 2: Combine like terms by adding or subtracting:
Combining the terms with "k", we have:
9k + 5k = 14k.
Combining the constant terms, we have:
3 - 10 = -7.
So the simplified expression is:
14k - 7.
9(k+1/3) + 10(1/2k-1)
= 9k + 3 + 10(1/2k-1)
= 9k + 3 + 10/2k - 10
= 9k + 3 + 5/k - 10
= 9k + 5/k - 7