Sure, let's simplify the given expression step-by-step:
Given expression:
[tex]\[
-k + 2(-2k - 5)
\][/tex]
1. Start by distributing the coefficient 2 to each term inside the parentheses:
[tex]\[
2(-2k - 5) = 2 \cdot (-2k) + 2 \cdot (-5)
\][/tex]
Simplifying this, we get:
[tex]\[
= -4k - 10
\][/tex]
2. Now substitute this back into the original expression:
[tex]\[
-k + (-4k - 10)
\][/tex]
Which simplifies to:
[tex]\[
-k - 4k - 10
\][/tex]
3. Combine the like terms:
[tex]\[
-k - 4k = -5k
\][/tex]
So we have:
[tex]\[
-5k - 10
\][/tex]
Therefore, the simplified expression is:
[tex]\[
-5k - 10
\][/tex]
The correct answer is:
(B) [tex]\(-5k - 10\)[/tex]
