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Solving Inequalities

Solving Inequalities. Chapter 3. 3.1 Inequalities and Their Graphs. Pg. 164 – 170 Obj : Learn how to write, graph, and identify solutions of inequalities. Content Standard: Prepares for A.REI.3. 3.1 Inequalities and Their Graphs.

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Solving Inequalities

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  1. Solving Inequalities Chapter 3

  2. 3.1 Inequalities and Their Graphs • Pg. 164 – 170 • Obj: Learn how to write, graph, and identify solutions of inequalities. • Content Standard: Prepares for A.REI.3

  3. 3.1 Inequalities and Their Graphs • Solution of an inequality – any number that makes the inequality true • Representing Inequalities • < or > open circles • < or > closed circles

  4. 3.2 Solving Inequalities Using Addition or Subtraction • Pg. 171 – 177 • Obj: Learn how to use addition or subtraction to solve inequalities. • Content Standards: A.REI.3 and A.CED.1

  5. 3.2 Solving Inequalities Using Addition or Subtraction • Equivalent Inequalities – inequalities that have the same solutions • Solving Addition or Subtraction Inequalities • Isolate the variable • Do the opposite operation • Addition – Subtraction • Subtraction – Addition • Whatever you do to one side of the equation, you must do to the other

  6. 3.3 Solving Inequalities Using Multiplication or Division • Pg. 178 – 183 • Obj: Learn how to use multiplication or division to solve inequalities. • Content Standards: A.CED.1, N.Q.2, and A.REI.3

  7. 3.3 Solving Inequalities Using Multiplication or Division • Solving Multiplication or Division Inequalities • Isolate the Variable • Do the opposite operation • Multiplication – Division • Division – Multiplication • If you multiply or divide by a negative, change the direction of the inequality. • Whatever you do to one side, you must do to the other

  8. 3.3 Solving Inequalities Using Multiplication or Division • Concept Byte – Pg. 184 • Properties of Equality • Reflexive Property – a = a • Symmetric Property – If a=b, then b=a • Transitive Property – If a=b and b=c, then a=c • Transitive Property of Inequality • If a<b and b<c, then a<c

  9. 3.4 Solving Multi-Step Inequalities • Pg. 186 – 192 • Obj: Learn how to solve multi-step inequalities. • Content Standards: Prepares for A.REI.3 and A.CED.1

  10. 3.4 Solving Multi-Step Inequalities • Solving Inequalities • Use the Distributive Property to remove any grouping symbols • Combine like terms on each side of the inequality • Get the variable terms on one side of the inequality and the constants on the other • Solve for the variable • Check your solution in the original inequality

  11. 3.5 Working With Sets • Pg. 194 – 199 • Obj: Learn how to write sets and identify subsets and find the complement of a set. • Content Standard: A.REI.3

  12. 3.5 Working With Sets • Roster Form – lists the elements of a set within braces {} – {2,4,6,8,…} • Set-builder notation – describes the properties an element must have to be in included in a set – {x|x is a multiple of 2} – “the set of all real numbers x, such that x is a multiple of 2” • Empty Set – the set that contains no elements • Universal Set – the largest set you are using • Complement of a Set – the set of all elements in the universal set that are not in the set (A’)

  13. 3.6 Compound Inequalities • Pg. 200 – 206 • Obj: Learn how to solve and graph inequalities containing the words “and” or “or”. • Content Standards: A.REI.3, and A.CED.1

  14. 3.6 Compound Inequalities • Compound Inequality – consists of two distinct inequalities joined by the and or the word or • Interval notation • Parentheses – Use (or) when a < or > symbol indicates that the interval’s endpoints are not included • Brackets – Use [or] when a < or > symbol indicates that the interval’s endpoints are included • Infinity – Use ∞ when the interval continues forever in a positive direction. Use -∞ when the interval continues forever in a negative direction.

  15. 3.7 Absolute Value Equations and Inequalities • Pg. 207 – 213 • Obj: Learn how to solve equations and inequalities involving absolute value. • Content Standards: A.CED.1, and A.SSE.1.b

  16. 3.7 Absolute Value Equations and Inequalities • Solving Absolute Value Equations • Set what is inside the absolute signs equal to both the positive and negative values • Solve each equation and check your solutions • Solving Absolute Value Inequalities • Use method similar to absolute value equations • < or < is an “and” compound inequality • > or > is an “or” compound inequality

  17. 3.8 Unions and Intersections of Sets • Pg. 214 – 220 • Obj: Learn how to find the unions and intersections of sets. • Content Standard: A.CED.1

  18. 3.8 Unions and Intersections of Sets • Union – the set that contains all elements of the sets (A ∪ B) • Intersection – the set of elements that are common to every set (A ∩ B) • Disjoint Sets – sets that have no elements in common

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