Question

How do you do this inequality?: 2/5k-4/15>-2/3

Answer 1

For this case we have the following inequality:

`\frac {2} {5} k- \frac {4} {15}> - \frac {2} {3}`

To solve, we follow the steps below:

We add
`\frac {4} {15}`to both sides of the inequality:

`\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}`

We multiply by 5 on both sides of the inequality:

`2k> - \frac {2} {5} * 5\\2k> -2`

We divide between 2 on both sides of the inequality:

`k> - \frac {2} {2}\\k> -1`

Thus, the solution is given by all values of k greater than -1.

ANswer:

`k> -1`