Chapter 4

Equations, Inequalities and Graphs

Modulus (absolute value) equations and quadratic inequalities — with an interactive exercise.

Equations, Inequalities and Graphs includes quadratic inequalities and the modulus (absolute value).

The modulus $|x|$ is the size of $x$ ignoring its sign, so $|-7|=7$. The equation $|x|=5$ has two solutions, $x=5$ and $x=-5$.

Remember

  • $|x|$ is always $\ge 0$.
  • $|x|=k$ (for $k>0$) has two solutions.

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