Question

solve for k.
10k - 8 ≥ 8k - 2
write your answer with k first, followed by an inequality symbol.

Explanation:

Step1: Subtract \(8k\) from both sides

To isolate the terms with \(k\), we subtract \(8k\) from each side of the inequality \(10k - 8\geq8k - 2\). This gives \(10k-8k - 8\geq8k - 8k- 2\), which simplifies to \(2k - 8\geq - 2\).

Step2: Add 8 to both sides

Next, we add 8 to both sides of the inequality \(2k - 8\geq - 2\) to isolate the term with \(k\). So, \(2k-8 + 8\geq - 2+8\), which simplifies to \(2k\geq6\).

Step3: Divide by 2

Finally, we divide both sides of the inequality \(2k\geq6\) by 2. Since we are dividing by a positive number, the direction of the inequality sign remains the same. So, \(\frac{2k}{2}\geq\frac{6}{2}\), which simplifies to \(k\geq3\).

Answer:

\(k \geq 3\)