How to Solve and Graph Double Inequalities

Miacademy & MiaPrep Learning Channel

This educational mathematics video provides a clear, step-by-step guide to understanding and solving double inequalities, also known as compound inequalities without connecting words. Hosted by an instructor named Kailey, the video breaks down the visual and algebraic meaning of expressions like "36 < x < 48" and "-3 ≤ 2x - 1 ≤ 5". It emphasizes that these mathematical statements function as "AND" inequalities, meaning the variable must satisfy two conditions simultaneously. The video explores key algebraic themes including translating algebraic expressions onto number lines, understanding the difference between strict inequalities (<) and inclusive inequalities (≤), and procedural fluency in solving multi-step equations. A significant portion of the video demonstrates two distinct methods for solving complex double inequalities: breaking them into separate parts and solving them simultaneously as a single unit. It visually reinforces these concepts by plotting solution sets on number lines, distinguishing clearly between open and closed circles. For educators, this resource serves as an excellent visual aid for Algebra I units on inequalities. It effectively addresses common student stumbling blocks, such as knowing when to use solid versus open dots on a number line and how to perform algebraic operations on three parts of an inequality at once. The use of color-coding (orange and blue) to distinguish between the two bounds helps students visually parse the structure of compound inequalities, making abstract algebraic concepts more concrete and accessible.