REVIEW: Year 1: D. Linear equations and inequalities: 20. Revisiting Linear Equation Solving

Lesson: Revisiting Linear Equation Solving

Introduction

Solving linear equations is a fundamental skill in algebra that lays the groundwork for understanding more complex mathematical concepts. These equations, which represent straight-line relationships, pop up in various real-world contexts, from economics to physics. This lesson will review the methods for solving linear equations and provide online resources for practice and mastery.

Objectives

• Refresh the knowledge of solving linear equations.
• Practice solving these equations using different methods.
• Utilize online exercises for skill enhancement and problem-solving practice.

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Reviewing Methods to Solve Linear Equations

1. Simple Linear Equations:
   • Equations like $ax+b=c$ can be solved by isolating the variable $x$.
   • Example: Solve $2x+3=7$ by subtracting 3 from both sides and then dividing by 2.
2. Equations with Variables on Both Sides:
   • In equations like $ax+b=cx+d$, collect all variable terms on one side and constant terms on the other.
   • Example: Solve $3x+4=5x-2$ by rearranging the terms to isolate $x$.
3. Using the Distributive Property:
   • For equations with parentheses, use the distributive property to expand the terms before solving.
   • Example: Solve $2(3x-4)=12$ by first expanding and then solving for $x$.
4. Checking Solutions:
   • After finding the solution, substitute it back into the original equation to verify its correctness.

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Online Resources for Linear Equation Practice

Several online platforms offer interactive exercises to practice solving linear equations:

1. Khan Academy (Khan Academy Linear Equations):
   • Provides a range of problems with step-by-step solutions and explanations.
   • Offers practice exercises with instant feedback.
2. IXL Learning (IXL Algebra Practice):
   • Offers interactive questions with a variety of linear equations.
   • Tailors problems to your skill level and provides detailed explanations.

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Exercise

• Solving Different Types of Equations: Pick a mix of linear equations, including some with variables on both sides and others requiring the use of the distributive property. Solve them and use online resources to check your solutions.
• Real-Life Applications: Formulate real-world problems that can be represented by linear equations, such as calculating distances, budgeting, or even simple physics problems. Solve these problems and verify your answers using the online platforms.

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Conclusion

Revisiting and practicing the solving of linear equations solidifies a key aspect of algebra. These equations are not just academic exercises but tools that can be applied to decipher various real-world situations. By using online resources for practice, you can enhance your problem-solving skills and deepen your understanding of linear relationships. Keep exploring these concepts, and you’ll find a wide range of applications in both academic studies and everyday life.