Mathematics (AS)·Algebra · NSSCAS 2.1.1
Modulus equations & inequalities
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In this lesson Miss Eve shows you what the modulus sign really means — the distance of a number from zero. You will solve modulus equations two ways, by the plus-minus split and by squaring both sides, and learn to check for false answers. You will also solve modulus inequalities, picturing each one on a number line as a middle band or as two outer regions. By the end the two upright bars will feel friendly and familiar.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.1.1):
- Interpret and use the modulus notation |x| as the distance of x from zero, with the piecewise definition.
- Solve modulus equations using the ± split and using |a| = |b| ⇔ a² = b², checking for extraneous roots.
- Solve modulus inequalities using |x − a| < b ⇔ a − b < x < a + b, and handle the greater-than case as two regions.
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