Section 3-1 Inequalities and Their Graphs.
Objectives: To write, graph & identify solutions of Inequalities.
Solution of the Inequality: any number that makes the Inequality true.
Inequality Symbols: < Less Than ≤ Less Than or Equal To > Greater Than ≥ Greater Than or Equal To
< , > open circle on the number line. ≤ , ≥ solid dot on the number line.
How to say the Inequality:
All Real Numbers greater than or equal to two.
How to Read the Inequality: 2 > x Read the Variable first. All Real Numbers less than two. Section 3-2 Solving Inequalities Using Addition & Subtraction.
Objectives: To use addition and subtraction to solve Inequalities.
Equivalent Inequalities: Inequalities with the same solutions. Section 3-3 Solving Inequalities Using Multiplication & Division.
Objectives: To use multiplication and division to solve inequalities.
Rule: When solving an Inequality, if you multiply or divide both sides of the Inequality by a NEGATIVE number, switch the direction of the Inequality Symbol. Section 3-4 Solving Multi-Step Inequalities.
Objectives: To solve multi-step Inequalities.
1)Distribute if possible to remove any parentheses.
2)Combine like terms if possible.
3)Use the addition or subtraction property of equality to move the variables to one side of the equation.
4)Use the addition or subtraction property of equality to get the term with the variable alone on one side of the equation.
5)Use the multiplication or division property of equality to get the variable by itself on one side of the equation.
6)Graph the solution on a number line. Section 3-5 CC: Working with Sets.
Objectives: To write sets and identify subsets. To find the complement of a set.
Roster Form: lists the elements of a set within { }.
Set – Builder Notaion: it describes the properties an element must have to be included in the set. Example: {x|x is a multiple of 2}
Empty Set: the set that contains no elements.
Universal Set: the largest set.
Complement of a Set: is the set of all elements in the universal set that are NOT in the set. Section 3-6 Compound Inequalities.
Objectives: To solve and graph Inequalities containing “and”. To solve and graph Inequalities containing “or”.
Compound Inequality: Two Inequalities joined by the word “and” or the word “or”.
Conjunction: Two Inequalities joined by the word “and”. Solutions of a conjunction MUST work for BOTH of the Inequalities.
< , ≤ - are conjunctions. Disjunction: Two Inequalities joined by the word “or”. Solutions of a disjunction can work for one Inequality, or the other Inequality, or both of the Inequalities.
> , ≥ - are disjunctions.
Section 3-7 CC: Absolute Value Equations and Inequalities.
Objectives: To solve equations & inequalities that contain absolute value.
Procedures for Solving an Equation that Involves Absolute Value:
1) Get the absolute value by itself on one side of the equation. 2) If the absolute value is equal to a Negative number, the answer is No Solution. 3) If not, write two equations. A) The first equation is the same without the absolute value symbols. B) The second equation is the same as the first equation but the number by itself is changed to a negative. 4) Solve both of the equations. Procedures for Solving an Inequality that Involves Absolute Value:
1) Get the absolute value by itself on one side of the Inequality. 2) Determine if the Inequality is a Conjunction or a Disjunction. 3) Write two Inequalities. A) The first Inequality is the same without the absolute value symbols. B) The second Inequality is the same as the first inequality but change the direction of the inequality symbol and make the number by itself the opposite. 4) Solve both of the Inequalities. 5) Graph it on a number line.