Unit 2: Multi-Step Equations & Inequalities

Introduction

• Focus on solving multi-step equations and inequalities.
• Emphasis on understanding and applying different mathematical methods.

Key Concepts

Multi-Step Equations

• Definition: Equations that require more than one operation (addition, subtraction, multiplication, division) to solve.
• Steps to Solve:
  1. Simplify each side of the equation (e.g., distribute and combine like terms).
  2. Use inverse operations to isolate the variable.
  3. Check solution by substituting back into original equation.

Inequalities

• Definition: Mathematical sentences that show the relationship between quantities that are not equivalent (e.g., >, <, ≥, ≤).
• Solving Inequalities:
  • Similar steps as solving equations.
  • Important rule: When multiplying or dividing by a negative number, reverse the inequality sign.

Application

• Real-world problems can often be modeled with equations and inequalities.
• Practice includes word problems requiring the setup and solution of equations and inequalities.

Techniques and Strategies

• Distributive Property: Used to simplify expressions.
• Combining Like Terms: Simplifies expressions to make solving easier.
• Inverse Operations: Key to isolating the variable.

Tips for Success

• Always perform the same operation on both sides of the equation/inequality.
• Keep the equation/inequality balanced.
• Double-check solutions by substituting back into the original equation/inequality.
• Pay attention to special rules for inequalities (especially with negative multipliers).

Conclusion

• Mastery of multi-step equations and inequalities is crucial for progress in mathematics.
• Understanding these concepts aids in solving complex mathematical problems and applying math in real-world scenarios.