Modulus & Inequality Traps
Test the steps that decide whether an inequality has been solved or merely rearranged — squaring, multiplying, and what a modulus actually allows.
Fourteen questions cover |x| < a against |x| > a, when squaring both sides is legitimate, why dividing by a negative flips the sign, why √(x²) is |x| and not x, the triangle inequality, and the method of intervals for rational inequalities.
Includes the denominator zeros that stay excluded even when the inequality is non-strict.
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Sample questions3 of 14 shown
Q1
A student is told that a > 0 and writes: "|x| < a simply means x < a". What is the correct equivalent statement?
Q2
With a > 0, a student converts |x| > a into the double inequality −a < x < a. Which conversion is actually correct?
Q3
While solving an inequality, a student squares both sides without checking anything. Under which condition is squaring both sides of an inequality a legitimate (equivalence-preserving) step?
What This Quiz Covers
- |x| < a against |x| > a
- When squaring both sides is legitimate
- Multiplying by an expression of unknown sign
- √(x²) = |x|, not x
- Triangle inequality and its equality case
- Method of intervals and excluded denominators
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