WEEK 10-SOLVING-AND-GRAPHING-LINEAR-INEQUALITIES

Solving and Graphing Linear Inequalities

Start

Objectives

Two Step Linear Inequalities

Summary

Compound Inequalities

Linear Inequalities

Introduction

Introduction

Linear Inequalities

is a variable

Here:

a,b

are any three numbers.

is a variable

An inequality shows the relationship between two expressions that are not equal.

🗨️

ax+b>0, ax+b≥0, ax+b<0, ax+b≤0.

Definition: A linear inequality is a statement in any of these basic forms:

If a<b,c>0:

Properties of <,>,

If a<b, c>0then ac>bc

If a<b,c<0:

Properties of Inequalities

Let a, b, c be real numbers, the following properties hold:

If a<bthen a-c<b-c

If a<b,c>0then ac<bc

If a<bthena+c<b+c

a<b, b<cthen a<c

Try it by yourself:

Two Step Linear Inequalities

x<2

2x + 1 < 5

Example 1: Two step inequality. Solve and plot the solution set.

Let's see some examples:

2x-1≥4

Example 1: Two step inequality. Solve and plot the solution set.

Let's see some examples:

2x-1≥4

x=5

Example 3: Three times a number added to 10 equals 25. Find the number.

Example 2: Solve

Let's see some examples:

Compound Inequalities

x=2, 2.5, 3 and 4 are some possible solutions.

Example 1: A twice a number x added with 1 is between 3 and 9. Find the solution set, graph it and list some possible solutions.

1≤x≤4

Compound inequalities occur when two inequalities are satisfied simultaneously.

🗨️

Try it by yourself:

Try it by yourself:

Divisionc>0: a/c<b/cc<0: a/c>b/c

Subtractiona-c<b-c

Multiplicationc>0: ac<bcc<0: ac>bc

Additiona+c<b+c

Summary: Solving Inequalities

8TH-SOLVING-AND-GRAPHING-LINEAR-INEQUALITIES-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

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Welcome 6th graders!

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A compass.
• A Protactor.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

MATERIAL

It is highly advised to have:

"MA.8.AR.2 Solve multi-step one-variable equations and inequalities." MA.8.AR.2.2 Solve two-step linear inequalities in one variable and represent solutions algebraically and graphically. MA.K12.MTR.6.1 Assess the reasonableness of solutions. MA.K12.MTR.2.1 "Demonstrate understanding by representing problems in multiple ways."

Solve inequality (ies)

Using properties of inequalities

Plot the solution on a number line

It's always a good a idea to visualize possible solutions in a diagram

Check the Solution

Whether it makes sense or no. Checking validity for some values.

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State restrictions/conditions in the form of inequalities

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