Solving Equations with the Distributive Property and Inverse Operations

🔑 Key Concepts

  • Solve equations by undoing operations in a logical order.
  • Use the distributive property to remove parentheses before isolating the variable when needed.
  • Look for efficient first steps, such as dividing both sides by a common factor.
  • Keep equations balanced by performing the same operation on both sides.
  • Check the solution by substituting it into the original equation.

✏️ Worked Examples — Solving Multi-Step Equations

🧠 Math Vocabulary

  • Inverse operations: Operations that undo one another, such as addition and subtraction or multiplication and division.
  • Coefficient: The number multiplying a variable.
  • Distributive property: Multiplying a factor by every term inside parentheses.
  • Isolate: To get the variable alone on one side of an equation.
  • Equivalent equations: Equations that have the same solution.
  • Substitution: Replacing a variable with a value to check whether an equation is true.

💡 Main Idea

To solve an equation, simplify when necessary and use inverse operations to isolate the variable. Some equations are most efficiently solved by adding or subtracting first, while equations with a common factor outside parentheses may be simplified by dividing both sides first. The goal is always to keep the equation balanced while producing simpler equivalent equations.

📚 What You Should Already Know

Before this lesson, students should understand integer operations, inverse operations, and basic one-step and two-step equations. Students should also know how multiplication relates to division and how to evaluate an expression by substituting a value for the variable.

🚀 What Comes Next

After solving equations like these, students can move into equations involving distribution, combining like terms, variables on both sides, and fractional coefficients. These same strategies also support work with 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.