1. **State the problem:** Solve the inequality $2x - 3 \leq 11$. 2. **Write the inequality:** $$2x - 3 \leq 11$$ 3. **Add 3 to both sides to isolate the term with $x$:** $$2x - 3 + 3 \leq 11 + 3$$ $$2x \leq 14$$ 4. **Divide both sides by 2 to solve for $x$:** $$\frac{2x}{2} \leq \frac{14}{2}$$ $$x \leq 7$$ 5. **Interpretation:** The solution to the inequality is all values of $x$ less than or equal to 7. 6. **Graphical representation:** On a number line from 0 to 9, shade all points from 0 up to 7, including 7, and extend the shading to the left indefinitely (since the inequality includes all $x \leq 7$).