Solution: We begin with the inequality:

Sat, 18 Apr 2026 23:51:18 +0000

# Unlocking Solutions: Mastering Inequalities in Problem-Solving When confronted with complex mathematical challenges, one of the most powerful starting points is the inequality. Whether you're modeling real-world scenarios, optimizing systems, or exploring abstract functions, solving inequalities equips you with critical reasoning and analytical tools. In this article, we'll dive deep into how beginning with an algebraic inequality serves as a foundational solution in both physics, engineering, economics, and everyday decision-making. ## Why Start with an Inequality? Inequalities are not just restrictions—they represent boundaries within which solutions exist. They help define feasible regions, compare magnitudes, and evaluate certainty under uncertainty. Unlike equations that yield exact values, inequalities reveal ranges of possible outcomes, making them indispensable in optimization problems, risk assessment, and scientific modeling.