Use the properties of operations to add 9 (k+1/3) + 10 (1/2k-1)

Answer 1

To add the expressions 9(k + 1/3) and 10(1/2k - 1), we can distribute the numbers outside the parentheses to the terms inside the parentheses and then combine like terms.

First, distribute 9 to (k + 1/3):

9(k + 1/3) = 9k + 9(1/3) = 9k + 3

Next, distribute 10 to (1/2k - 1):

10(1/2k - 1) = 10(1/2k) - 10(1) = (10/2k) - 10 = 5/k - 10

Now we add the two expressions together:

(9k + 3) + (5/k - 10)

To simplify this further, we can combine like terms:

9k + 3 + 5/k - 10

Rearranging the terms, we have:

9k + 5/k + 3 - 10

Now, let's simplify each part separately:

9k + 5/k is not like terms, so it cannot be combined further.

3 - 10 = -7

Therefore, the simplified expression is:

9k + 5/k - 7