Use the properties of operation to add 9(k +1/3 + 10(1/2k - 1)
To simplify the expression 9(k + 1/3) + 10(1/2k - 1), we can use the distributive property of multiplication over addition/subtraction.
9(k + 1/3) + 10(1/2k - 1) becomes:
9 * k + 9 * (1/3) + 10 * (1/2k) - 10 * 1
Now, let's simplify each term separately:
9 * k simplifies to 9k,
9 * (1/3) simplifies to 3,
10 * (1/2k) simplifies to 5/k,
-10 * 1 simplifies to -10.
The simplified expression becomes:
9k + 3 + 5/k - 10.
To add 9(k + 1/3) + 10(1/2k - 1), we will use the distributive property of multiplication over addition.
Step 1: Distribute 9 over the terms inside the parentheses:
9 * k = 9k
9 * (1/3) = 3
So, the expression becomes:
9k + 3 + 10(1/2k - 1)
Step 2: Distribute 10 over the terms inside the parentheses:
10 * (1/2k) = 10/(2k) = 5/k
10 * (-1) = -10
So, the expression becomes:
9k + 3 + 5/k - 10
Step 3: Combine like terms:
The terms 9k and -10 cannot be combined since they have different variables (k and a constant, respectively). But the terms 3 and 5/k can be combined since they have the same variable (k).
Therefore, the final expression is:
9k + 5/k + 3 - 10
Note: If there are any additional instructions or simplification needed, please let me know.
To simplify the expression 9(k + 1/3) + 10(1/2k - 1), we need to apply the distributive property and combine like terms.
Let's start by simplifying the expression within the parentheses:
k + 1/3 = k * 1 + 1/3 = k + 1/3
1/2k - 1 = (1/2)k - 1 = (1/2k) - 1
Now, we can rewrite our expression:
9(k + 1/3) + 10(1/2k - 1) = 9k + 9(1/3) + 10(1/2k) - 10(1)
Next, we can simplify each term separately:
9k = 9k
9(1/3) = 3
10(1/2k) = 10/2k = 5/k
-10(1) = -10
Now, let's rewrite the expression with the simplified terms:
9(k + 1/3) + 10(1/2k - 1) = 9k + 3 + 5/k - 10
Finally, we can combine like terms by adding or subtracting coefficients with the same variable:
9k + 3 - 10 + 5/k = 9k - 7 + 5/k
Therefore, the simplified expression is: 9k - 7 + 5/k