Question

1. 4(k - 2) = 2(k - 9)

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b - c)=ab - ac\), we expand the left side \(4(k - 2)\) to \(4k-8\) and the right side \(2(k - 9)\) to \(2k-18\). So the equation becomes \(4k - 8=2k - 18\).

Step2: Subtract \(2k\) from both sides

Subtract \(2k\) from each side to get \(4k-2k - 8=2k-2k - 18\), which simplifies to \(2k - 8=-18\).

Step3: Add 8 to both sides

Add 8 to both sides: \(2k-8 + 8=-18 + 8\), resulting in \(2k=-10\).

Step4: Divide by 2

Divide both sides by 2: \(\frac{2k}{2}=\frac{-10}{2}\), so \(k = - 5\).

Answer:

\(k=-5\)