Use the properties of operations to add 9(k+1/3)+10(1/2k−1)
To simplify the expression 9(k+1/3) + 10(1/2k - 1), we will first distribute the coefficients:
9(k+1/3) + 10(1/2k-1) = 9k + 9(1/3) + 10(1/2k) + 10(-1)
Next, we will simplify each term:
9k + 9(1/3) is equal to 9k + 3
And 10(1/2k) is equal to (10/1) * (1/2k) = 10/(2k) = 5/k
Finally, we have:
9k + 3 + 5/k - 10
Now, we can combine like terms:
(9k - 10) + (5/k + 3)
Thus, the simplified expression is 9k - 10 + 5/k + 3.
To add the expression 9(k+1/3) + 10(1/2k-1), we can use the distributive property to simplify.
Starting with the first term, 9(k+1/3):
1. Distribute 9 to both terms inside the parentheses:
9k + 9 * 1/3.
Simplifying further, 9 * 1/3 is equal to 3, so the expression becomes:
9k + 3.
Moving on to the second term, 10(1/2k-1):
2. Distribute 10 to both terms inside the parentheses:
10 * 1/2k - 10 * 1.
Simplifying further, 10 * 1/2k is equal to 5k, and 10 * 1 is equal to 10, so the expression becomes:
5k - 10.
Now, we have the simplified forms of both terms, 9k + 3 and 5k - 10.
3. Combine like terms:
(9k + 3) + (5k - 10).
Combining like terms, we simply add the coefficients of k separately and add the constant terms separately.
Adding the coefficients of k, 9k + 5k is equal to 14k.
Adding the constant terms, 3 + (-10) is equal to -7.
Therefore, the final simplified expression is:
14k - 7.
To simplify the expression 9(k+1/3) + 10(1/2k-1) using the properties of operations, we will follow these steps:
Step 1: Distribute (multiply) 9 to each term inside the parentheses, and distribute 10 to each term inside the parentheses.
9(k + 1/3) + 10(1/2k - 1)
= 9 * k + 9 * (1/3) + 10 * (1/2k) - 10 * 1
Step 2: Simplify the expressions that result from distributing.
= 9k + 9/3 + 10/2k - 10
= 9k + 3 + 5/k - 10
Step 3: Combine like terms, which means adding or subtracting terms that have the same variable and exponent.
= 9k + 5/k - 7
So, the simplified form of the expression 9(k+1/3) + 10(1/2k-1) is 9k + 5/k - 7.