Question

1. 1 - 11(k - 1) = -12(k - 2) - 9

Explanation:

Step1: Expand both sides

Expand the left - hand side: \(1-11(k - 1)=1-11k + 11=12-11k\)
Expand the right - hand side: \(-12(k - 2)-9=-12k + 24-9=-12k + 15\)
So the equation becomes \(12-11k=-12k + 15\)

Step2: Solve for k

Add \(12k\) to both sides of the equation:
\(12-11k + 12k=-12k + 15+12k\)
\(12 + k=15\)
Subtract 12 from both sides:
\(k=15 - 12\)
\(k = 3\)

Answer:

\(k = 3\)