Warm Up Solve each inequality. 1. x + 3 ≤ 10 2. x ≤ 7 23 < –2x + 3

Slides:

Advertisements

Similar presentations

Solving Compound Inequalities

Advertisements

3-6 Compound Inequalities

Essential Question: How do you solve a system of inequalities by graphing?

Systems of Linear Inequalities.  Two or more linear inequalities together form a system of linear inequalities.

3.3 Graphing Systems of Inequalities. Steps to Graphing a System of Inequalities. 1) Graph each inequality with out shading the region. 2) Find the region.

Find the set of integers that is greater than 2 and less than 7 Find the set of integers that is greater than 2 or less than 7 How do the use of the words.

Warm-Up Evaluate each expression, given that x=3 and y=-2. a. |2x -9| Answer: 1) -32) 33) 154) -15 b. |y –x| Answer: 1) -52) 13) -14) 5 Solve. |3x + 6|

CHAPTER 1 – EQUATIONS AND INEQUALITIES 1.6 – SOLVING COMPOUND AND ABSOLUTE VALUE INEQUALITIES Unit 1 – First-Degree Equations and Inequalities.

Objectives: Graph the solution sets of compound inequalities. Solve compound inequalities. Standards Addressed: C: Create and interpret inequalities.

A compound statement is made up of more than one equation or inequality. A disjunction is a compound statement that uses the word or. Disjunction: x ≤

Aim: How do we solve Compound Inequalities? Do Now: Solve the following inequalities 1. 2x + 3 > x < 10 How do we put two inequalities together?

Compound Inequalities “And” & “Or” Graphing Solutions.

5.4 – Solving Compound Inequalities. Ex. Solve and graph the solution.

Compound Inequalities Chapter 4.8 Part 1. Definition Compound Inequalities are two inequalities joined by the words “and” or “or”.

Set Operations and Compound Inequalities. 1. Use A = {2, 3, 4, 5, 6}, B = {1, 3, 5, 7, 9}, and C = {2, 4, 6, 8} to find each set.

Warm-Up: Solve and Graph  1.  2.  3.. CHAPTER 6 SECTION 3 Solving Compound Inequalities.

Solving Linear Inequalities `. Warm-up -4 < x ≤ 6 x ≤ -4 or x>

Compound Inequalities

Compound Inequalities – Day 1 October 1, x  -12 (-12,  ) x ≤ 9 (- , 9] SWBAT: Solve and graph solutions sets of compound inequalities with one.

Solving Linear Inequalities Lesson 5.5 linear inequality: _________________________________ ________________________________________________ solution of.

Solving Open Sentences Involving Absolute Value

Solve: 1. |x – 4| = 9 2.|7x – 2| = 5 3.|3x – 2| + 4 = 21 Write the inequality shown: WU 36.

Warm Up Solve |x – 5| = 4 x – 5 = 4 or x – 5 =

Warm Up Write a compound inequality for each graph. Remember include “AND” “OR” in your answer

CHAPTER 1 – EQUATIONS AND INEQUALITIES 1.6 – SOLVING COMPOUND AND ABSOLUTE VALUE INEQUALITIES Unit 1 – First-Degree Equations and Inequalities.

Essential Question: How do you solve a system of inequalities by graphing?

Linear Inequalities by Graphing

M3 1.5 Systems of Linear Inequalities M3 1.5 Systems of Linear Inequalities Essential Questions: How can we write and graph a system of linear inequalities.

9.2 Compound Sentences Standard 5.0, 24.0 Standard 5.0, 24.0 Two Key Terms Two Key Terms.

Warm-Up Let A = {0,1,3,8}, B = {2,4,5,6,7,9}, and C = {0,1,8}. 4 minutes Find the following sets.

Chapter 6 – Solving and Graphing Linear Inequalities 6.3 – Solving Compound Inequalities.

Warm Up 1.) You start growing flowers from seed and plan to sell them potted for Mother’s Day. It cost you $1.75 to pot and grow each plant. If you sell.

Math on the Mind: Solve –2 2x – 4 < 6. Graph the solution. < 1 x < 5

9.2 Compound Sentences Goal(s): Solve and Graph Conjunctions and Disjunctions.

Lesson 15: Compound Inequalities Objectives: Describe the solution set of two inequalities joined by either “and” or “or” and graph the solution set on.

Chapter 3: Solving Inequalities

Chapter 2: Equations and Inequalities Section 2.3/2.4: Conjunctions and Disjunctions and Solving Compound Sentences with Inequalities.

Alg2 Lesson 1-4 Solving Inequalities Objectives: 1.Solve inequalities. 2.Solve combined inequalities. 3.Identify conjunctions and disjunctions. 4.Graph.

Solving Systems of Inequalities n You will simply be graphing two inequalities on the same graph. n The solution will be a section of the graph, not a.

Notes Over 1.6 Solving an Inequality with a Variable on One Side Solve the inequality. Then graph your solution. l l l

Show a graph of each expression All real numbers that are between –4 and 6 All real numbers that are at least 2, but at most 6 A length between 2 cm and.

Chapter 1 Lesson 6 Solving Compound and Absolute Value Inequalities.

Lesson 2-6: Compound Inequalities

1-4 Solving Inequalities

3.3 – Solving Systems of Inequalities by Graphing

Objectives Solve compound inequalities with one variable.

Solving Systems of Inequalities: 3 - 4

Absolute Value inequalities

Solve Absolute Value Inequalities

Warm Up Graph y = 4x and 16, $10’s and 7 $20’s.

Warm Up Solve each inequality. 1. x + 3 ≤ x ≤ 7 23 < –2x + 3

Lesson Objective: I will be able to …

Algebra 1 Section 4.4.

2.5 Solving Compound Inequalities

Graphing Inequalities

Aim: How do we solve Compound Inequalities?

5-4 Compound Inequalities

Solve Systems of Linear Inequalities

Compound Inequalities and their Graphs

Algebra 1 Section 4.5.

Warm Up Graph y = 4x and 16, $10’s and 7 $20’s.

Quadratic Systems. What you’ll learn

WU 36 Solve: 1. |x – 4| = 9 |7x – 2| = 5 |3x – 2| + 4 = 21

Algebra 1B – Name: _________________________

4 minutes Warm-Up Solve..

Warm-Up #27 1) 2x + 2y= 2 x - y = 3 use substitution 2) Evaluate f x = −x 2 −3x+12;x=2 3) Use f(x) = −4x 2 + x -13 and h(x) 2x + 5; find (f−h)

Solving Compound Inequalities

Warm Up: Solve and graph: -8p > 24 9z + 2 > 4z + 15.

Solving Inequalities Lesson 1-5 Part 2

Presentation transcript:

Warm Up Solve each inequality. 1. x + 3 ≤ 10 2. x ≤ 7 23 < –2x + 3 x < –10 Solve each inequality and graph the solutions. 4. 4x + 1 ≤ 25 x ≤ 6 5. 0 ≥ 3x + 3 x ≤ –1

Solving compound Inequalities Lesson 2-6 Solving compound Inequalities You'll Learn how to solve compound inequalities. graph the solution sets of compound inequalities.

Which of these applicants meet the requirements? RPS will hire a new Teacher that’s tall AND good looking Alex: 166 cm John: 186 cm Sam: 183 cm Which of these applicants meet the requirements? He is tall AND good looking

Which of these applicants meet the requirements? RPS will hire a new Teacher that’s tall OR good looking Alex: 166 cm John: 186 cm Sam: 183 cm Which of these applicants meet the requirements? All of them Every applicant is either tall OR Good looking

Definition A compound inequality consists of two inequalities connected by the words: AND (conjunction) OR (disjunction)

1 solve compound inequalities (conjunction/and) 3x – 5 > 7 and EXAMPLE 1 Solve and graph 3x – 5 > 7 and 8x – 14 ≤ 66 Solve both inequalities for x 8x ≤ 66 + 14 3x > 7 + 5 8x ≤ 80 3x > 12 8 8 3 3 x ≤ 10 x > 4 Graph the solution The Solution is the (double shaded) region 2 –6 –4 –2 6 4 –8 8 10 12 –10 –12 4 < x ≤ 10

Solve the conjunction for x EXAMPLE 2 Solve and graph -1 < x + 3 < 2 Solve the conjunction for x -3 -3 -3 -4 < x < -1 Graph the solution 1 –3 –2 –1 3 2 –4 4 5 6 –5 –6

3 solve compound inequalities (disjunction/or) 2x + 3 < –7 Or EXAMPLE 3 Solve and graph 2x + 3 < –7 Or 4x – 10 ≥ – 2 Solve both inequalities for x 4x ≥ –2 + 10 2x < –7 – 3 4x ≥ 8 2x < -10 4 4 2 2 x ≥ 2 x < -5 Graph the solution The Solution is (All shaded) regions 1 –3 –2 –1 3 2 –4 4 5 6 –5 –6

-2x + 1 ≥ 3 and 3x – 4 ≤ 17 x – 2 > – 4 or x + 2 < 5 Your Turn Solve and graph 1 -2x + 1 ≥ 3 and 3x – 4 ≤ 17 2 x – 2 > – 4 or x + 2 < 5 3 -5 < 2x – 3 ≤ 11

Homework Page 138 – 139 #s: 16-all-26, 36-all-40 + 48, 49 and 50