1. **Stating the problem:** We are asked to solve an inequality problem related to consumer arithmetic. 2. **General approach:** Inequalities are solved similarly to equations but with special rules when multiplying or dividing by negative numbers. 3. **Key rule:** When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed. 4. **Example problem:** Suppose we want to solve the inequality $$3x - 5 > 7$$. 5. **Step 1:** Add 5 to both sides to isolate the term with $x$: $$3x - 5 + 5 > 7 + 5$$ $$3x > 12$$ 6. **Step 2:** Divide both sides by 3 (positive number, so inequality sign stays the same): $$\frac{3x}{3} > \frac{12}{3}$$ $$x > 4$$ 7. **Interpretation:** The solution means $x$ must be greater than 4 for the inequality to hold true. 8. **Summary:** - Add or subtract terms to isolate the variable term. - Divide or multiply by the coefficient of the variable, reversing the inequality sign if the number is negative. - Write the solution set accordingly. This method applies to consumer arithmetic problems involving inequalities, such as budget constraints or price comparisons.