Use an inequality and the five-step process to solve each...

Use an inequality and the five-step process to solve each problem.
Refer to Exercise $57 .$ If Abriana's rental car gets $30 \mathrm{mpg},$ how many miles must she drive in order to make the first option more economical?

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Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two expressions that are not necessarily equal, using symbols like <, >, ?, or ?. They are used to express constraints or conditions in problems, such as when comparing different costs or outcomes to determine which option is more economical.

Five-Step Process for Solving Problems

This process guides you through solving problems systematically. It involves understanding the problem, defining variables, formulating the inequality (or equation), solving the inequality, and then checking that the solution fits the context of the problem. This structured approach is critical for breaking down and solving complex word problems in an organized manner.

Break-Even Analysis

Break-even analysis involves determining the point at which two different cost options result in the same expense, beyond which one option becomes more economical than the other. It is commonly used in cost comparison scenarios to find the threshold where switching from one option to another becomes financially advantageous.

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