1. **Stating the problem:** We want to understand how to solve linear inequalities and then apply that knowledge to solve given inequality problems. 2. **What is a linear inequality?** A linear inequality is similar to a linear equation but instead of an equals sign, it uses inequality signs like $<$, $\leq$, $>$, or $\geq$. 3. **General rules for solving linear inequalities:** - You can add or subtract the same number from both sides without changing the inequality. - You can multiply or divide both sides by a positive number without changing the inequality. - If you multiply or divide both sides by a negative number, you must reverse the inequality sign. 4. **Example:** Solve $2x + 3 < 7$ Step 1: Subtract 3 from both sides: $$2x + 3 - 3 < 7 - 3$$ $$2x < 4$$ Step 2: Divide both sides by 2 (positive number, so inequality stays the same): $$\frac{2x}{2} < \frac{4}{2}$$ $$x < 2$$ 5. **Now, solving the first question from Exercise 14.3 part (a):** $x < 5$ This inequality means $x$ can be any number less than 5. 6. **Number line representation:** Draw a line with an open circle at 5 (because 5 is not included) and shade all numbers to the left. 7. **Summary:** To solve linear inequalities, isolate the variable using addition, subtraction, multiplication, or division, remembering to flip the inequality sign if multiplying or dividing by a negative number. This explanation prepares you to solve the inequalities in Exercise 14.3.