Algebra · Inequalities
Chapter 1 · 3
The idea
Quadratic inequalities
Why x² < 16 has TWO boundaries, how the parabola sketch decides "between" versus "outside", and why two-region answers must be written with "or" — never chained into one impossible inequality.
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Algebra · Inequalities
Quadratic inequalities
Why x² < 16 has TWO boundaries, how the parabola sketch decides "between" versus "outside", and why two-region answers must be written with "or" — never chained into one impossible inequality.
Why it works
Squares keep two boundaries
tempts a one-line answer: "". But test : is false — yet . Squaring wipes out signs, so BIG negative numbers have big squares too. The truth has two boundaries:— is trapped between the two square roots, negative side included. Every quadratic inequality has this shape: two boundary values and a question of which side(s) of them the answer lives.
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The rest of the explanation, plus 2 worked examples you step through move by move.
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