Table of Contents

1. Introduction
2. Balancing Equations
   1. What is Balancing?
   2. Example: Balancing an Equation
3. Simplifying Equations
   1. What is Simplifying?
   2. Example: Simplifying an Equation
4. Practice

Introduction

In this section, we'll learn about balancing and simplifying algebraic equations. These are crucial techniques for solving equations effectively.

Balancing Equations

What is Balancing?

• Balancing an equation means ensuring that the expressions on both sides of the equation are equal.
• It involves adding, subtracting, multiplying, or dividing both sides of the equation by the same amount.

Example: Balancing an Equation

• Consider the equation: \( x + 3 = 7 \).
• To balance, subtract the constant 3 from both sides: \( x + 3 - 3 = 7 - 3 \), which simplifies to \( x = 4 \).

Simplifying Equations

What is Simplifying?

• Simplifying an equation means reducing it to its simplest form.
• This often involves combining like terms and eliminating unnecessary parts.

Example: Simplifying an Equation

• Consider the equation: \( 2x + 3x - 5 = 6 \).
• Combine like terms: \( 5x - 5 = 6 \).

Practice

• Balance and solve the equation: \( 2x + 5 = 3x + 2 \).
• Simplify and solve the equation: \( 4x + 2x - 10 = 12 \).