Use the properties of operations to add 9 (k +1/3) +10 (1/2 k -1). (1 Point)
Responses
14k + 13
14k - 2/3
14k - 7
19 1/2 k - 2/3
To simplify the expression, first distribute each term of the first parentheses to the terms in the second parentheses:
9(k) + 9(1/3) + 10(1/2k) - 10(1)
This simplifies to:
9k + 3 + 5k - 10
Now, combine like terms:
(9k + 5k) + (3 - 10)
This further simplifies to:
14k - 7
So the answer is 14k - 7.
To add 9(k + 1/3) + 10(1/2k - 1), we can distribute the multiplication across the terms inside the parentheses:
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 = 5k - 10
Now we can combine like terms:
9k + 3 + 5k - 10 = (9k + 5k) + (3 - 10) = 14k - 7
Therefore, the simplified expression is 14k - 7.
To add the given expressions, we need to simplify and combine like terms.
First, let's distribute the coefficients to the terms inside the parentheses:
9(k + 1/3) = 9k + 9/3 = 9k + 3
10(1/2 k - 1) = 10(1/2 k) - 10(1) = 5k - 10
Now, we can add the simplified expressions:
(9k + 3) + (5k - 10)
To combine like terms, add the coefficients of the k terms and the constant terms separately:
9k + 5k = 14k
3 - 10 = -7
Therefore, the simplified expression is:
14k - 7
So, the correct answer is 14k - 7.