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

Answer 1

To simplify the expression \(9\left(k + \frac{1}{3}\right) + 10\left(\frac{1}{2}k - 1\right)\), we can use the distributive property to expand both terms:

1. Distribute the 9: \[ 9\left(k + \frac{1}{3}\right) = 9k + 9 \cdot \frac{1}{3} = 9k + 3 \]

2. Distribute the 10: \[ 10\left(\frac{1}{2}k - 1\right) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10 \]

Now, combine the two results: \[ 9k + 3 + 5k - 10 \]

Next, combine like terms (the terms with \(k\) and the constant terms): \[ (9k + 5k) + (3 - 10) = 14k - 7 \]

Thus, the simplified expression is: \[ \boxed{14k - 7} \]