Inequalities
Bayani Gaba-gaba
Equations tell you exactly where two expressions are equal, but in mathematics and real life you often need to know where one quantity is larger or smaller than another. Inequalities give you a way to describe entire ranges of values, not just single solutions, and they appear throughout the 4PM1 specification whenever a question asks for a set of values rather than a point.
You will learn to solve linear and quadratic inequalities algebraically, represent linear inequalities in two variables on a coordinate grid, and tackle introductory linear programming problems. Every technique builds on algebra you already know, with a few critical sign rules that catch out even confident students.
Manufura
- Solve simple linear and quadratic inequalities
- Represent linear inequalities in two variables graphically
- Solve simple problems on linear programming
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Takardar Darasi
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Nazarin Darasi
Barka da kammala darasi akan Inequalities. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- Solve 3x - 5 > 7. A) x > 4 B) x > 2 C) x < 4 D) x > 12 Answer: A
- Which values of x satisfy x^2 - 4x - 5 < 0? A) x < -1 or x > 5 B) -1 < x < 5 C) x < -5 or x > 1 D) -5 < x < 1 Answer: B
- When solving an inequality, what must you do if you divide both sides by a negative number? A) Nothing changes B) Reverse the inequality sign C) Square both sides D) Add 1 to both sides Answer: B
- In a linear programming problem, the optimal value of the objective function occurs at: A) The centre of the feasible region B) Any point on a boundary line C) A vertex of the feasible region D) The origin Answer: C
- The boundary line for the inequality 2x + y < 6 should be drawn as: A) A solid line B) A dashed line C) A dotted line with arrows D) A double line Answer: B
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
Systems of Nonlinear Equations and Inequalities: Two Variables
Solve a system of nonlinear equations using substitution.
"College Algebra: Systems of Nonlinear Equations and Inequalities: Two Variables" 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/7-3-systems-of-nonlinear-equations-and-inequalities-two-variables. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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