Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To add the expression 9(k + 1/3) + 10(1/2k - 1), we can use the distributive property and combine like terms.

First, distribute 9 to both terms inside the parentheses:
9 * k + 9 * (1/3) + 10(1/2k - 1)

This simplifies to:
9k + 3/3 + 10(1/2k) + 10(-1)

Since 3/3 is equal to 1, we can write:
9k + 1 + 10(1/2k) - 10

Now distribute 10 to both terms inside the parentheses:
9k + 1 + 10/2k - 10

Simplifying further, we have:
9k + 1 + 5k - 10

Combine like terms:
14k - 9

Therefore, 9(k + 1/3) + 10(1/2k - 1) simplifies to 14k - 9.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression 9(k+1/3)+10(1/2k−1), we can distribute the terms and then combine like terms. Let's break down the steps:

Step 1: Distribute 9 to (k + 1/3):
9(k+1/3) = 9k + 9(1/3)
= 9k + 3

Step 2: Distribute 10 to (1/2k - 1):
10(1/2k−1) = 10(1/2k) − 10(1)
= 10/2k − 10
= 5/k − 10

Step 3: Combine the terms:
9k + 3 + 5/k - 10

Step 4: Simplify further if needed:
9k + 5/k - 7

Therefore, the simplified expression is 9k + 5/k - 7.

Answer 3

[AI-generated answer — Explain Bot]

To add the expression 9(k + 1/3) + 10(1/2k - 1), we can distribute the coefficients to the terms within parentheses and then combine like terms. Here's how you can do it step by step:

Step 1: Distribute the coefficient of 9 to the terms inside the first set of parentheses and the coefficient of 10 to the terms inside the second set of parentheses:

9(k + 1/3) + 10(1/2k - 1)
= 9k + 9(1/3) + 10(1/2k) - 10(1)

Step 2: Simplify any multiplication involving fractions:

9(1/3) = 9/3 = 3
10(1/2k) = 10/2k = 5/k

The expression now becomes:

9k + 3 + 5/k - 10

Step 3: Combine like terms. In this case, the like terms are the ones with variables (k) and the ones without variables.

The terms with the variable k are 9k and 5/k:

9k + 5/k

The terms without the variable k are 3 and -10:

3 - 10

Thus, we have:

9(k + 1/3) + 10(1/2k - 1) = 9k + 5/k - 7

Note: Please keep in mind that depending on the context or any specific instructions, there might be additional simplification or transformation steps required.