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2. Linear Equations in One Variable

Linear equations in one variable are algebraic equations where the highest power of the variable is one. This chapter addresses techniques for solving such equations, including those with variables on both sides and methods for reducing equations to simpler forms. The importance of understanding linear equations is emphasized, as they are foundational for solving a variety of real-life problems.

Sections

Linear Equations in One Variable

This section introduces linear equations in one variable, explaining their characteristics and methods for solving them.

2 Section Overview

Start current section content and materials

2.1 Introduction

This section introduces linear equations in one variable, discussing basic concepts and definitions related to algebraic expressions and equations.

2.2 Solving Equations having the Variable on both Sides

This section focuses on solving equations with variables on both sides, detailing methods and providing examples.

2.3 Reducing Equations to Simpler Form

This section explains how to reduce equations, particularly those involving fractions and variables, to simpler forms for easier solution finding.

Learning Objectives

  • An algebraic equation is an equality involving variables, indicating the equivalence of the expressions on both sides.

  • Linear equations in one variable are characterized by containing only one variable that is not raised to a power greater than one.

  • To solve equations, one can perform equivalent operations on both sides while maintaining the equality.

Key Concepts

Algebraic Equation

An equation involving variables and an equality sign, representing that the two sides are equal in value.

Linear Equation

An equation where the highest power of the variable is one, typically appearing in the form ax + b = c.

Solution

The value(s) of the variable(s) that make an equation true.

Transposing

The act of moving a term from one side of an equation to another while changing its sign.

Reducing Equations

The process of simplifying an equation to make it easier to solve, often by eliminating fractions or combining like terms.

Practice Exercises

Total Questions

6

Estimated Time

12 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting