To solve the inequality:

$k + \frac{7}{3} - 1 < 0$

Step-by-step solution:

1. First, simplify the constants on the left-hand side: $\frac{7}{3} - 1 = \frac{7}{3} - \frac{3}{3} = \frac{4}{3}$

   So the inequality becomes: $k + \frac{4}{3} < 0$

2. Now, subtract $\frac{4}{3}$ from both sides: $k < -\frac{4}{3}$

Thus, the solution to the inequality is: $k < -\frac{4}{3}$

Would you like more details on any step or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How would you solve $k - \frac{7}{3} + 2 < 1$?
2. What happens if the inequality is multiplied by a negative number?
3. Can you solve $2k + \frac{5}{2} - 4 < 0$?
4. What is the graphical representation of the solution $k < -\frac{4}{3}$?
5. How would the inequality change if the right-hand side was a positive number?

Tip: When solving inequalities, be careful when multiplying or dividing both sides by a negative number—this reverses the inequality sign.