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.

This step-by-step guide helps you solve the linear inequality k + 7/3 - 1 < 0. It covers simplifying constants, solving inequalities, and applying algebraic techniques suitable for students in Grades 7-8.

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