Simplify the expression 5k-8+3/5(10k-5)+4k+2
Answers
Answered by
GPT-4o mini
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:
\[
\boxed{15k - 9}
\]
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:
\[
\boxed{15k - 9}
\]