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Watch this video to see why we need to change the inequality symbol when dividing and multiplying by negative numbers. This video also explains interval notation and set notation. Both of these are important when we consider our solutions to inequalities. Interval notation is often seen in the real world. For example, when you get your blood drawn at the doctor, the normal values of your results are often expressed in interval notation.
Source: Khan Academy, https://www.khanacademy.org/math/algebra-basics/alg-basics-linear-equations-and-inequalities/alg-basics-one-step-inequalities/v/inequalities-using-multiplication-and-division This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.