Use properties of operation to add

Question

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

Answer 1

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

1. Distribute \(9\) into the first term: \[ 9(k + \frac{1}{3}) = 9k + 9 \cdot \frac{1}{3} = 9k + 3 \]

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

Now, we can combine both results: \[ 9k + 3 + 5k - 10 \]

3. Combine like terms:
   • The \(k\) terms: \(9k + 5k = 14k\)
   • The constant terms: \(3 - 10 = -7\)

So, the simplified expression is: \[ 14k - 7 \]