For this case we have the following inequality:
[tex]\frac {2} {5} k- \frac {4} {15}> - \frac {2} {3}[/tex]
To solve, we follow the steps below:
We add [tex]\frac {4} {15}[/tex]to both sides of the inequality:
[tex]\frac {2} {5} k> - \frac {2} {3} + \frac {4} {15}\\\frac {2} {5} k> \frac {15 * (- 2) + 3 * 4} {15 * 3}\\\frac {2} {5} k> \frac {-30 + 12} {45}\\\frac {2} {5} k> \frac {-18} {45}\\\frac {2} {5} k> \frac {-2} {5}\\\frac {2} {5} k> - \frac {2} {5}[/tex]
We multiply by 5 on both sides of the inequality:
[tex]2k> - \frac {2} {5} * 5\\2k> -2[/tex]
We divide between 2 on both sides of the inequality:
[tex]k> - \frac {2} {2}\\k> -1[/tex]
Thus, the solution is given by all values of k greater than -1.
ANswer:
[tex]k> -1[/tex]
