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: $$\boxed{{\displaystyle 15k-9}}$$