2. Linear Equations in One Variable

2. Linear Equations in One Variable

  • 2

    Linear Equations In One Variable

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

  • 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.

    • Key Summary

    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.

    Key Takeaways

    • 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.