To solve the inequality 2/3k - 6 < 24, we can start by adding 6 to both sides of the inequality:
2/3k - 6 + 6 < 24 + 6
Simplifying the left side gives:
2/3k < 30
To isolate k, we can multiply both sides by 3/2:
2/3k * 3/2 < 30 * 3/2
Simplifying the left side gives:
k < 45
Therefore, the inequality 2/3k - 6 < 24 expressed in its simplest form is k < 45.