Solving Multi-Step Equations

🔑 Key Concepts

  • Choose an efficient first step based on the structure of the equation.
  • Clear a denominator by multiplying both sides by the denominator.
  • Use the distributive property before combining like terms.
  • Apply integer rules carefully when distributing negative numbers.
  • Use inverse operations to isolate the variable.
  • Keep the equation balanced by performing the same operation on both sides.

✏️ Worked Examples — Solving Multi-Step Equations Efficiently

🧠 Math Vocabulary

  • Distributive property: Multiplying a factor by every term inside parentheses.
  • Like terms: Terms that contain the same variable raised to the same power.
  • Coefficient: The number multiplying a variable.
  • Inverse operations: Operations that undo one another, such as addition and subtraction.
  • Equivalent equations: Equations that have the same solution.
  • Isolate: To get the variable alone on one side of an equation.

💡 Main Idea

This lesson focuses on choosing an efficient sequence of steps for solving multi-step equations. Some equations begin by clearing a denominator, while others require distributing a positive or negative factor and combining like terms. After simplifying, use inverse operations to isolate the variable while keeping both sides of the equation balanced.

📚 What You Should Already Know

Before this lesson, students should understand inverse operations, integer rules, the distributive property, and how to combine like terms. They should also be comfortable solving one-step and two-step equations and multiplying both sides of an equation by the same number.

🚀 What Comes Next

Next, students will solve equations involving variables on both sides, fractional coefficients, and more complex combinations of distribution and like terms. These strategies also prepare students for solving inequalities, formulas, and algebraic word problems.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.