Modulus Inequalities
Gbogbo ọrọ náà
A modulus inequality asks not for an exact distance from zero, but for a range of distances: which values lie within a certain reach, or beyond it. The answer is always an interval or a pair of intervals, and once you see the distance picture, deciding which is effortless.
In this lesson you will solve \(|x|
Ebumnobi
- Solve, graphically or algebraically, inequalities involving the modulus, such as k|ax + b| > c and k|ax + b| <= |cx + d|.
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Ekele diri gi maka imecha ihe karịrị na Modulus Inequalities. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
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- Solve |x - 3| < 2. A. x < 1 or x > 5 B. 1 < x < 5 C. -5 < x < -1 D. x < 5 Answer: B
- The inequality |x| > c (c > 0) is equivalent to: A. -c < x < c B. x < -c or x > c C. x > c only D. x < c Answer: B
- Solve |2x - 1| > 5. A. -2 < x < 3 B. x < -2 or x > 3 C. x > 3 only D. -3 < x < 2 Answer: B
- Solve 3|x + 1| < 12. A. -5 < x < 3 B. x < -5 or x > 3 C. -4 < x < 4 D. -3 < x < 5 Answer: A
- Which is a valid way to write the solution of |x| > 4? A. -4 > x > 4 B. x < -4 or x > 4 C. -4 < x < 4 D. x = 4 Answer: B
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Linear Inequalities and Absolute Value Inequalities
Use interval notation
"College Algebra: Linear Inequalities and Absolute Value Inequalities" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/2-7-linear-inequalities-and-absolute-value-inequalities. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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