Inequalities.

Slides:



Advertisements
Similar presentations
Solving Linear Inequalities
Advertisements

© 2002 by Shawna Haider. There are two kinds of notation for graphs of inequalities: open/filled-in circle notation and interval notation brackets. 64.
Inequalities Graphing and solving.
2.4 – Linear Inequalities in One Variable
Linear Inequalities in one variable Inequality with one variable to the first power. for example: 2x-3
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Inequalities. Equation Inequality A statement that asserts the equality of 2 terms A relationship between 2 terms that are of unequal value Contains an.
Math 021. * Interval Notation is a way to write a set of real numbers. The following are examples of how sets of numbers can be written in interval notation:
Equations and Inequalities
Solving Inequalities Solving Inequalities Objective: SWBAT solve and graph compound inequalities.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Equations and Inequalities Chapter 2.
Solving Compound inequalities with OR. Equation 2k-5>7 OR -3k-1>8.
§ 2.8 Solving Linear Inequalities. Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Linear Inequalities in One Variable A linear inequality in one.
4.1 Solving Linear Inequalities
Review your homework with your partner. Be ready to ask questions!!! Friday!!!!
Inequalities in One Variable.  Use the same process for solving an equation with TWO exceptions: ◦ 1) Always get the variable alone on the LEFT side.
Solving Linear Inequalities MATH 018 Combined Algebra S. Rook.
Solving Inequalities: Review of Unit 12 Created by: Amanda Hollenbacher 1/30/2005.
Chapter P Prerequisites: Fundamental Concepts of Algebra 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.9 Linear Inequalities and Absolute.
Review #1. SOLVING LINEAR EQUATIONS, INEQUALITIES AND ABSOLUTE VALUES  Multi-Step Equations  Solve each equation. Check your solution.  1) 4x – 12.
Inequalities Symbols and line graphs. Symbols  < is less than  > is greater than  < is less than or equal to  > is greater than or equal to points.
4.1.1 – Solving Inequalities. All equations we have solved are considered problems of equality – Involves some kind of equal sign On the other hand, we.
Day Problems For each solution write and graph an inequality.
Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.
Solve the following equations for x: 1) 2) 3) 4) 5) 6)
Solving Linear Inequalities and Compound Inequalities.
Unit 1: Functions 1-2: Inequalities, Set-Builder Notation, and Interval Notation.
Inequalities R eview- g reater than: greater than or equal to: less than: less than or equal to: ** The inequality sign is always pointing to the smaller.
Final Exam Review of Inequalities
Thinking Mathematically Algebra: Equations and Inequalities 6.4 Linear Inequalities in One Variable.
1.4 Solving Inequalities I can: 1.Graph inequalities 2.Solve inequalities.
One Step Inequalities Review. Adding Negative Numbers: Same signs add and keep the sign Different signs subtract and keep the sign of the larger Subtracting.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 2 Equations, Inequalities and Problem Solving.
Intro to Inequalities Unit 4 Section 4.1. Definition A statement that a mathematical expression is greater than or less than another expression.
September 20, 2011 At the end of today, you will be able to Solve inequalities and compound inequalities Warm-up: Solve for x 1.│5x│ - 38 = x +
Section 2.5 Linear Inequalities in One Variable (Interval Notation)
Two-step Inequalities SOL 8.15 cont.. What is an inequality? An inequality is a mathematical sentence that compares expressions using: < less than > greater.
Solving One-Step Inequalities
CHAPTER 6 SECTION 2B Solving Inequalities- variable on both sides.
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Linear Inequalities in One Variable.
Section 2.6 Solving Linear Inequalities and Absolute Value Inequalities.
Solving inequalities. An equation. Solve this and graph the answer on a number line: x - 2 = 5.
Lesson 2-4: Solving Inequalities Objective Students will solve and graph inequalities using addition/subtraction/multiplication/division and check that.
Solving Inequalities   Trichotomey Property- For any two real numbers, a and b, exactly one of the following statements is true: a b.  Set-Builder.
1.6 Solving Linear Inequalities
Solving Absolute Value Inequalities
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
2.1/2.2 Solving Inequalities
Solving & Graphing Inequalities
Algebra: Equations and Inequalities
3-6 Compound Inequalities
Inequalities Objective: Students will be able to solve, graphing and write inequalities with one variable and apply them to real world situations.
B5 Solving Linear Inequalities
Solving Inequalities Equations
Solving Inequalities Equations
6.1 to 6.3 Solving Linear Inequalities
6.1 to 6.3 Solving Linear Inequalities
Lesson 2-4: Solving Inequalities
2.1 Solving Linear Inequalities
2.1 – 2.2 Solving Linear Inequalities
3-6 Compound Inequalities
Lesson 1 – 5 Solving Inequalities.
Inequalities and their Graphs
Solving Linear Inequalities
Solving Inequalities Equations
Section 3.1 Inequalities – Solve and Graph Inequalities
Presentation transcript:

Inequalities

Symbols: < less than > Greater than ≤ less than or equal to ≥ greater than or equal to Example: X > 4 Solution of an inequality is a value of the variable that makes the inequality true. An inequality has MORE THAN ONE solution.

When we have an inequality we represent it 2 different ways: 1). An inequality statement x ≤ 6 2). A picture Always use an arrow at the end!

How to make an inequality a picture First: If you have the symbol greater than or less than you an OPEN CIRCLE If you have the symbol greater than or equal to or less than or equal to you use a closed circle Practice: 1). X > -7 2). F ≥ -2 3). -6 < h

Solving inequalities Same rules and steps as solving equations ONE EXCEPTION THOUGH: When you multiply or divide BOTH SIDES by a negative number you must flip the inequality sign Why? -3x > 9

Solve the inequalities and graph the solution. 1). 3x > -12 2). 2x – 6 < 9 3). -14 ≤ 2(2x -4) 4). -6x – 3 > -4(x +1)

Think about what numbers can be a solution for this statement: -6 < x < 10

Compound inequalities There is more than one solution, but the solutions are in between two real numbers Graphing compound solutions -6 < x < 10

Solving Compound Inequalities We must perform the same operation to ALL 3 PARTS -6 < 2x + 4 < 12 -4 -4 -4 -10 < 2x < 8 2 2 2 -5 < x < 4 Now graph the compound inequality

Interval Notation for Compound Inequalities -5 < x < 4 No infinity symbols (-5, 4) In order from least to greatest. Examples: Solve the compound inequalities, graph the solution, and write the interval notation 1). -24 ≤ 3x < 9 2). 4 < 3x – 8 < 24 3). -4< 2(x-3) ≤ 4

∞ positive infinity -∞ negative infinity The third way we represent inequalities is interval notation If your arrow is going to the right you use positive infinity If your arrow is going to the left you use negative infinity If you have ≥ or ≤ then your number will have a bracket If you have > or < then your number will have a parentheses ∞ positive infinity -∞ negative infinity Infinity always has parentheses!!! Practice: 1). X > -7 2). F ≥ -2 3). -6 < h