Unit 4: Equations and Inequalities

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Master the art of solving equations and inequalities, graphing solutions, and understanding mathematical relationships

🎯 7 Sections⏱️ 50-65 min📈 Graphing

Unit 4 Overview

In this unit, you're going to learn a whole lot about equations and inequalities and how to solve them. You'll be able to figure out when an equation or inequality is describing a situation, and you'll be able to tell when an equation or inequality just doesn't cut it.

You will also learn to graph the solution for inequalities on the number line and know how the values work to give the result. Let's think about the ways equations and inequalities can help us describe relationships between things that depend on other things, such as time and distance, or cost and quantity.

We shall also use tables, graphs, and simple models to illustrate such relations and derive solutions that follow from particular models. Dive into the world of equations and inequalities. There are lots of helpful tips and practice problems in this section to help you become a problem-solving champ!

Learning Objectives

Solve one-step equations using addition, subtraction, multiplication, and division
Understand inequalities and how they differ from equations
Graph inequalities on a number line with proper symbols
Identify dependent and independent variables in relationships
Translate word problems into algebraic equations and solve them

Your Progress

Unit Overviewvideo

Solving One-Step Equationsvideo

Understanding Inequalitiesvideo

Graphing Inequalitiesvideo

Dependent and Independent Variablesvideo

Translating Words to Equationsvideo

Practice Problemspractice

Unit 4 Quizquiz

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Solving One-Step Equations

What You'll Learn:

Understanding what an equation is and what it means to solve an equation
Using addition, subtraction, multiplication, and division to isolate the variable
Solving one-step equations with positive and negative numbers
Checking solutions to ensure they are correct

Khan Academy - One-Step Equations

This video from Khan Academy introduces how to solve one-step equations using addition, subtraction, multiplication, and division. Clear examples make it easy to follow along.

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Math Antics - Solving Basic Algebraic Equations Part 1

This video from Khan Academy introduces how to solve one-step equations using addition, subtraction, multiplication, and division. Clear examples make it easy to follow along.

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Math Antics - Solving Basic Algebraic Equations Part 2

Part 2 of this series focuses on solving one-step equations using multiplication and division. It helps students understand how to isolate the variable.

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Understanding Inequalities

What You'll Learn:

What are inequalities and how they differ from equations
Symbols of inequalities: >, <, ≥, ≤
Writing inequalities to describe situations
Solving one-step inequalities using addition, subtraction, multiplication, and division
Interpreting solutions of inequalities

Khan Academy - Intro to Inequalities

This video introduces the concept of inequalities, showing how to solve and graph inequalities on a number line. It provides a strong foundation with clear examples.

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Math Antics - Solving Inequalities

This video from Math Antics explains what inequalities are and how they are used in real life. It covers basic inequalities, explaining how to solve and graph them with simple examples.

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Graphing Inequalities

What You'll Learn:

Representing inequalities on a number line
Understanding open and closed circles for less than/greater than vs. less than or equal to/greater than or equal to
Graphing solutions of one-step inequalities
Solving and graphing combined inequalities (AND/OR)

Khan Academy - Graphing Linear Inequalities

This video introduces how to graph linear inequalities on a coordinate plane, explaining the concepts of shaded regions and boundary lines. It covers both solid and dashed lines for inequalities.

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Mathispower4u - Graphing Linear Inequalities

This video provides step-by-step instructions on how to graph linear inequalities. It covers how to identify the inequality type, graph the boundary line, and shade the correct region.

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Dependent and Independent Variables

What You'll Learn:

Understanding the difference between dependent and independent variables
Identifying dependent and independent variables in word problems
Analyzing relationships between the two using tables, graphs, and equations

Khan Academy - Dependent and Independent Variables

This video explains the difference between dependent and independent variables using simple examples. It helps students understand how one variable affects the other in a mathematical relationship.

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Mathispower4u - Independent and Dependent Variables

This video provides a detailed explanation of dependent and independent variables, using clear, step-by-step examples. It is useful for students who want to understand how to identify these variables in various problems.

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Translating Words to Equations

What You'll Learn:

Understanding keywords that indicate mathematical operations (e.g., "sum" means addition, "product" means multiplication)
Converting word problems into algebraic equations
Identifying what each variable represents in a word problem
Solving the resulting equations

Khan Academy - Translating Word Problems

This video explains how to translate word problems into algebraic expressions, showing students how to identify keywords and set up equations correctly.

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The Organic Chemistry Tutor - Translating Word Problems

This video provides clear examples of how to turn word problems into algebraic expressions. It breaks down each problem step-by-step, making it easy to understand.

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