Solve and Graph 2x + 3 < 9 2x + 3 = x = x = 3

Slides:

Advertisements

Similar presentations

EXAMPLE 4 Graph a linear inequality in one variables Graph the inequality y  –3. SOLUTION Graph the equation y = –3. The inequality is , so use a solid.

Advertisements

9.4 – Solving Absolute Value Equations and Inequalities 1.

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0 3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2.

Graph the boundary line the same as if the problem was a linear equation.  Pretend that there is an equal sign and use an appropriate method to graph.

Kristie Ferrentino. 1. Find and graph the solution set of the inequality. 2. Determine the equation of a line that passes through the point (2,6) and.

 Linear Equations in Two Variables  To Graph a Linear Inequality 1)Graph the related linear equality (forms the boundary line).  and  are graphed.

A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution of a linear inequality is any.

Graphing Inequalities of Two Variables Recall… Solving inequalities of 1 variable: x + 4 ≥ 6 x ≥ 2 [all points greater than or equal to 2] Different from.

Essential Question: When graphing an inequality, how do you determine whether to include the boundary in the graph and which region to shade?

Linear Equations in One Variable

Graphs of Linear Inequalities When the equal sign in a linear equation is replaced with an inequality sign, a linear inequality is formed. Solutions of.

1) Graphing Linear Inequalities What linear inequality graphs look like… 1) boundary line (solid or dashed) 2) shaded area (above or below the boundary.

Chapter 3 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Linear Inequalities in Two Variables

1 Warm Up 1.Solve and graph |x – 4| < 2 2. Solve and graph |2x – 3| > 1 2x – x 4 x – 4 > -2 and x – 4 < x > 2 and x < 6.

Chapter 3 Section 4 Copyright © 2011 Pearson Education, Inc.

8.8 Linear Inequalities, Systems, and Linear Programming.

Lesson 2.10 Solving Linear Inequalities in Two Variables Concept: Represent and Solve Systems of Inequalities Graphically EQ: How do I represent the solutions.

Graphing Linear Inequalities in Two Variables A linear inequality in two variables takes one of the following forms: The solution of a linear inequality.

Graphing and Solving Inequalities. Finding an Inequality Boundary Boundary Point: A solution(s) that makes the inequality true (equal). It could be the.

2.8B Graphing Absolute Value Inequalities in the Coordinate Plane 1. Find location of the absolute value “V”  a I x – h I + k 2. Determine if graph is.

GOAL Graphing linear inequalities in two variables.

Good Morning Systems of Inequalities. Holt McDougal Algebra 1 Solving Linear Inequalities Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0 3. Write –6x.

Graphing a Linear Inequality

9.3 – Linear Equation and Inequalities 1. Linear Equations 2.

CHAPTER TWO: LINEAR EQUATIONS AND FUNCTIONS ALGEBRA TWO Section Linear Inequalities in Two Variables.

Graphing Inequality Systems

SystemsOfInequalities. 7-1 Solving Systems by Graphing What is a system of linear equations? “SOLUTION” No solution Infinitely Many Solutions Page 342.

3.3 Graphing and Solving Systems of Linear Inequalities.

Table of Contents Graphing Linear Inequalities in Two Variables A linear inequality in two variables takes one of the following forms: The solution of.

Chapter 3 Section 5. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Graphing Linear Inequalities in Two Variables Graph linear inequalities.

Graphing a Two Variable Inequality. Examining the Solutions of a Linear Equation Are the following points solutions to the equation y = -2x + 3 ? Justify.

9.5 Inequalities in Two Variables  Two Key Terms  Two Objectives.

Drill Explain how to graph the following line; y = 4x – 3.

Solving Systems of Equations Graphing Linear Inequalities.

Graphing Linear Inequalities in 2 Variables By Tristen Billerbeck.

Lesson 2.8 Graph Linear Inequalities in Two Variables.

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Inequalities and Absolute Value

Solving Linear Inequalities

Type Example Solution Linear equations 2x – 8 = 3(x + 5) A number in one variable x = -23.

Section 7.5 Systems of Linear Inequalities

1.8 Graphing Linear Inequalities

§ 9.4 Linear Inequalities in Two Variables and Systems of Linear Inequalities.

Graphing Linear Inequalities

Graphing Systems of Inequalities.

Chapter 3 Graphs and Functions

Chapter 3 Section 5.

Graphing a Linear Inequality in Two Variables

Graphing Linear Inequalities

2.6 Linear Inequalities in Two Variables

− −2 − −4 >5 2+4>5

Objective solve systems of linear inequalities in two variables.

Section 6.8 Linear Inequalities in Two Variables

Systems of Inequalities

Chapter 3 Section 4.

4 WARM UP GRAPH THE INEQUALITY (Lesson 1.4) x+5<− y > 19

Lesson Objective: I will be able to …

Linear Inequalities in Two Variables

Solutions of Equations and Inequalities

Chapter 3 Graphs and Functions.

Objective Graph and solve linear inequalities in two variables.

Graphing a Linear Inequality

Objective Graph Linear Equations and Linear Inequalities in Two Variables.

Linear Inequalities and Systems of Linear Inequalities

Graph Linear Inequalities in Two Variables

Solving Linear Inequalities

Learning Target Students will be able to: Graph and solve linear inequalities in two variables.

Systems of Inequalities

Presentation transcript:

Solve and Graph 2x + 3 < 9 2x + 3 = 9 -3 -3 2x = 6 2 2 x = 3 Solve a similar equation to find the dividing point. 2x + 3 = 9 -3 -3 2x = 6 2 2 x = 3 This is the dividing point. Plot in on the number line. Test a point. Test x = 0 -2 -1 0 1 2 3 4 5 2(0) + 3 < 9 0 + 3 < 9 x < 3 3 < 9 True. Write the solution. Shade the side with 0.

2.5: LINEAR INEQUALITIES Example: 5x – 2y  8 + 3x 5x – 2y = 8 + 3x 1. Write a similar _____________ . EQUATION –2y = -2x + 8 Replace < or > with =. –2 -2 -2 2. Solve for y. y = x - 4 This is your ___________ _______. BOUNDARY LINE y 6 3. Draw a graph. 4 4. Graph Boundary Line. 2 x DASHED Line if < or > SOLID Line if  or . -6 -4 -2 2 4 6 -2 -4 -6

False 5x – 2y  8 + 3x Test: (0, 0) 5(0) – 2(0)  8 + 3(0) 0  8 + 0 5. Test a point. 5(0) – 2(0)  8 + 3(0) Any point except points on dividing line. Identify your test point. Check in ORIGINAL problem. Show work when you substitute. Write True or False. 0  8 + 0 0  8 FALSE! x y 2 4 6 -2 -4 -6 6. Shade towards TRUTH. False Test Point TRUE: Shade SIDE w/ point. Test Point FALSE: Shade OTHER SIDE. 7. Write solution in y form. If below boundary line, then < or  If above boundary line, then > or  y ≤ x – 4

Graph the inequality Boundary line: Test point (0, 0) y-int: (0,-3) x 1 2 3 4 5 -1 -2 -3 -4 -5 Test point (0, 0) y-int: (0,-3) True Shade the side with (0, 0).

Graph the inequality Boundary line: Test point (0, 0) y-int: (0,1) x 1 2 3 4 5 -1 -2 -3 -4 -5 Boundary line: Test point (0, 0) y-int: (0,1) False