1. **State the problem:** We need to solve the inequality $3x - 2 < 10$ and represent its solution on a number line. 2. **Write the inequality:** $$3x - 2 < 10$$ 3. **Add 2 to both sides:** $$3x - 2 + 2 < 10 + 2$$ $$3x < 12$$ 4. **Divide both sides by 3:** $$\frac{\cancel{3}x}{\cancel{3}} < \frac{12}{3}$$ $$x < 4$$ 5. **Interpretation:** The solution is all values of $x$ less than 4. 6. **Graphing on a number line:** - Draw a horizontal line with tick marks. - Mark the point 4. - Shade the line to the left of 4. - Use an open circle at 4 to indicate that 4 is not included. This shows all $x$ such that $x < 4$. Final answer: $$x < 4$$