Modulus equations & inequalities
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Flip to reveal answersHow do you solve |inside| = c?
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All 8 Flashcards — Modulus equations & inequalities
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Question
How do you solve |inside| = c?
Answer
Set inside = +c and inside = −c (provided c ≥ 0), and solve both.
Question
What does |x| < a mean?
Answer
−a < x < a (a band around 0).
Question
What does |x| > a mean?
Answer
x < −a or x > a (everything outside the band).
Question
Can |something| equal a negative number?
Answer
No — a modulus is always ≥ 0, so |…| = (negative) has no solution.
Question
Solve |2x − 1| = 5.
Answer
2x − 1 = ±5 ⇒ x = 3 or x = −2.
Question
Solve |x − 2| < 3.
Answer
−3 < x − 2 < 3 ⇒ −1 < x < 5.
Question
How do you solve |f(x)| = |g(x)|?
Answer
f = g or f = −g (or square both sides).
Question
Solve |2x + 1| ≥ 4.
Answer
2x + 1 ≥ 4 or ≤ −4 ⇒ x ≥ 3/2 or x ≤ −5/2.
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Full study notes for Modulus equations & inequalities
Topic 2.16 hub
Modulus functions (HL only)
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