Question

2k + \frac{1}{3} > 1

Explanation:

Step1: Subtract $\frac{1}{3}$ from both sides

To isolate the term with \( k \), we subtract \(\frac{1}{3}\) from both sides of the inequality \( 2k+\frac{1}{3}>1 \). This gives us \( 2k+\frac{1}{3}-\frac{1}{3}>1 - \frac{1}{3} \), which simplifies to \( 2k>\frac{2}{3} \).

Step2: Divide both sides by 2

To solve for \( k \), we divide both sides of the inequality \( 2k>\frac{2}{3} \) by 2. Using the rule that dividing both sides of an inequality by a positive number does not change the direction of the inequality, we get \( k>\frac{\frac{2}{3}}{2} \). Simplifying the right - hand side, \(\frac{\frac{2}{3}}{2}=\frac{2}{3}\times\frac{1}{2}=\frac{1}{3}\).

Answer:

\( k > \frac{1}{3} \)