Question

1. 4k + 7(-4 - 2k) = -2(k - 2)

Explanation:

Step1: Expand the brackets

First, we expand the left - hand side: \(4k + 7(-4 - 2k)=4k-28 - 14k\), and the right - hand side: \(-2(k - 2)=-2k + 4\)
So the equation becomes \(4k-28 - 14k=-2k + 4\)

Step2: Combine like terms on the left

Combine the \(k\) terms on the left: \(4k-14k=-10k\), so the left - hand side is \(-10k-28\)
The equation is now \(-10k-28=-2k + 4\)

Step3: Move the \(k\) terms to one side

Add \(10k\) to both sides: \(-10k + 10k-28=-2k+10k + 4\), which simplifies to \(-28 = 8k+4\)

Step4: Solve for \(k\)

Subtract 4 from both sides: \(-28 - 4=8k+4 - 4\), so \(-32 = 8k\)
Then divide both sides by 8: \(k=\frac{-32}{8}=-4\)

Answer:

\(k = - 4\)