Alright, let's solve the given equation step by step to find the value of [tex]\( k \)[/tex].
The equation we are given is:
[tex]\[ 14 = -2(k + 8) \][/tex]
1. Distribute the [tex]\(-2\)[/tex] on the right side of the equation:
[tex]\[ 14 = -2k - 16 \][/tex]
2. Rearrange the equation to isolate the term containing [tex]\( k \)[/tex]. Add 16 to both sides of the equation to move the constant term to the left side:
[tex]\[ 14 + 16 = -2k \][/tex]
[tex]\[ 30 = -2k \][/tex]
3. To solve for [tex]\( k \)[/tex], divide both sides of the equation by [tex]\(-2\)[/tex]:
[tex]\[ k = \frac{30}{-2} \][/tex]
[tex]\[ k = -15 \][/tex]
So, the correct solution is:
[tex]\[ k = -15 \][/tex]
Given the multiple choice options:
- [tex]\( k = -15 \)[/tex]
- [tex]\( k = 11 \)[/tex]
- [tex]\( k = -11 \)[/tex]
- [tex]\( k = -3 \)[/tex]
The correct answer is:
[tex]\[ k = -15 \][/tex]
