We are solving the inequality:

\[
1 - 2x < -\frac{1}{3}
\]

### Step 1: Subtract 1 from both sides
To isolate the term with \(x\), subtract 1 from both sides of the inequality:

\[
1 - 2x - 1 < -\frac{1}{3} - 1
\]

This simplifies to:

\[
-2x < -\frac{1}{3} - \frac{3}{3}
\]

\[
-2x < -\frac{4}{3}
\]

### Step 2: Divide by -2
Now, divide both sides of the inequality by \(-2\), remembering that dividing by a negative number reverses the inequality sign:

\[
x > \frac{-\frac{4}{3}}{-2}
\]

Simplifying:

\[
x > \frac{4}{6} = \frac{2}{3}
\]

### Final Answer:
\[
x > \frac{2}{3}
\]

Let me know if you'd like more details or have any questions.

Here are 5 related questions to consider:
1. How do you solve inequalities with variables on both sides?
2. How does dividing or multiplying an inequality by a negative number affect it?
3. Can inequalities be graphed on a number line? How?
4. What are the differences between solving equations and inequalities?
5. How do compound inequalities work?

**Tip:** Always remember to reverse the inequality sign when dividing or multiplying by a negative number!

Learn how to solve the linear inequality 1 - 2x < -1/3 with a detailed step-by-step explanation. This solution covers essential algebraic concepts and highlights the importance of reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 7-9.

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