# Chapter 6: TE Graphing Linear Inequalities

**At Grade**Created by: CK-12

## Overview

In this chapter, students solve linear inequalities. They use the addition and multiplication properties of inequality and learn that the direction of the inequality is sometimes reversed when solving inequalities. Students solve single-step and multi-step inequalities and progress to compound inequalities and absolute value equations and inequalities. The chapter finishes with graphing inequalities in two variables.

Suggesting Pacing:

Inequalities Using Addition and Subtraction \begin{align*}1\;\mathrm{hr}\end{align*}

- Inequalities Using Multiplication and Division - \begin{align*}1\;\mathrm{hr}\end{align*}
- Multi-Step Inequalities - \begin{align*}1-2\;\mathrm{hrs}\end{align*}
- Compound Inequalities - \begin{align*}1-2\;\mathrm{hrs}\end{align*}
- Absolute Value Equations - \begin{align*}0.5\;\mathrm{hrs}\end{align*}
- Absolute Value Inequalities - \begin{align*}1\;\mathrm{hr}\end{align*}
- Linear Inequalities in Two Variables - \begin{align*}0.5\;\mathrm{hr}\end{align*}

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## Problem-Solving Strand for Mathematics

Teachers can increase students’ problem solving abilities by presenting them with challenging activities.

A Sudoku warm-up, used on a daily basis for a short period of time or once a week, can lead to excellent conversations on strategies. Solving problems together, students share their thinking and learn from each other. Furthermore, students can continue with Sudoku outside of class and practice various approaches.

Teachers can find Tiling Checkerboard Challenges or other thought-provoking brainteasers on the web and can easily differentiate them to meet the needs of students. Students can make progress with Checkerboard Tiling problems in many different ways. When asked, “Can an ordinary \begin{align*}8 \times 8\end{align*} checkerboard be covered by \begin{align*}31\end{align*} dominoes if two squares are removed?” students can sketch solutions, use paper tiles, use graph paper, or, more abstractly, simply consider the two-color arrangements on the checkerboard. There’s an entry point for every student, regardless of his or her mathematical background.

### Alignment with the NCTM Process Standards

Playing mathematically oriented games such as Sudoku, chess, Hex, Mudcracky, Five-In-a-Row, and Set can incorporate many of the NCTM process standards, particularly the Communication Standard. In a structured classroom setting, students will organize and consolidate their thinking (COM.1), communicate coherently and clearly to peers, teachers, and others (COM.2), and analyze and evaluate the thinking and strategies of others (COM.3). In addition, they will use representations to model and interpret physical phenomena (R.3). Both within and outside the classroom, students will apply and adapt a variety of appropriate strategies to solve problems (PS.3) and select and use various types of reasoning and methods of proof (RP.4).

- COM.1 - Organize and consolidate their mathematical thinking through communication.
- COM.2 - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
- COM.3 - Analyze and evaluate the mathematical thinking and strategies of others.
- PS.3 - Apply and adapt a variety of appropriate strategies to solve problems.
- RP.4 - Select and use various types of reasoning and methods of proof.
- R.3 - Use representations to model and interpret physical, social, and mathematical phenomena.

- 6.1.
## Inequalities Using Addition and Subtraction

- 6.2.
## Inequalities Using Multiplication and Division

- 6.3.
## Multi-Step Inequalities

- 6.4.
## Compound Inequalities

- 6.5.
## Absolute Value Equations

- 6.6.
## Absolute Value Inequalities

- 6.7.
## Linear Inequalities in Two Variables