To solve the inequality \( 1 - 2x < -\frac{1}{3} \), follow these steps:

1. **Subtract 1 from both sides:**
   \[
   1 - 2x - 1 < -\frac{1}{3} - 1
   \]
   Simplifying both sides:
   \[
   -2x < -\frac{1}{3} - \frac{3}{3}
   \]
   \[
   -2x < -\frac{4}{3}
   \]

2. **Divide both sides by -2**: 
   When dividing by a negative number, the inequality sign flips:
   \[
   x > \frac{-\frac{4}{3}}{-2}
   \]
   Simplifying:
   \[
   x > \frac{4}{6}
   \]
   \[
   x > \frac{2}{3}
   \]

Thus, the solution to the inequality is \( x > \frac{2}{3} \).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What happens when you multiply or divide inequalities by a negative number?
2. How would you graph the solution \( x > \frac{2}{3} \) on a number line?
3. Can you solve a similar inequality with fractions on both sides, like \( \frac{3x}{2} - 1 < \frac{5}{4} \)?
4. How would the solution change if the inequality was \( 1 - 2x \geq -\frac{1}{3} \)?
5. What are the properties of inequalities when working with absolute values?

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

Learn how to solve the inequality 1 - 2x < -1/3 step by step, using algebraic techniques. Understand how to manipulate inequalities and reverse the inequality sign when dividing by a negative number. This problem is suitable for Grades 6-8.

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