Simplify the expression 5k-8+3/5(10k-5)+4k+2

Answer 1

To simplify the expression \( 5k - 8 + \frac{3}{5}(10k - 5) + 4k + 2 \), we'll follow these steps.

1. Distribute \( \frac{3}{5} \) into \( (10k - 5) \): \[ \frac{3}{5}(10k - 5) = \frac{3}{5} \times 10k - \frac{3}{5} \times 5 = 6k - 3 \]

2. Substitute the result of the distribution back into the expression: \[ 5k - 8 + (6k - 3) + 4k + 2 \]

3. Combine the like terms. First, combine all the \( k \) terms: \[ 5k + 6k + 4k = 15k \]

4. Now combine the constant terms: \[ -8 - 3 + 2 = -9 \]

5. Putting it all together, we have: \[ 15k - 9 \]

Thus, the simplified expression is: \[ \boxed{15k - 9} \]