Solving Equations with Fractions and Variables on Both Sides

🔑 Key Concepts

  • Clear fractions by multiplying both sides by the least common denominator.
  • Use the distributive property when a factor appears outside parentheses.
  • Move variable terms to one side and constant terms to the other.
  • Combine like terms before isolating the variable.
  • Perform the same operation on both sides to keep the equation balanced.
  • Check solutions by substituting them into the original equation.

✏️ Worked Examples — Solving Fraction Equations with Variables on Both Sides

🧠 Math Vocabulary

  • Least common denominator: The smallest number that is a multiple of every denominator in an equation.
  • Fractional coefficient: A fraction that multiplies a variable.
  • Distributive property: Multiplying a factor by every term inside parentheses.
  • Like terms: Terms that contain the same variable raised to the same power.
  • Inverse operations: Operations that undo one another, such as addition and subtraction.
  • Isolate: To get the variable alone on one side of an equation.

💡 Main Idea

In this lesson, students solve equations containing fractions and variables on both sides of the equal sign. Multiplying both sides by the least common denominator removes the fractions and creates an equivalent equation that is easier to solve. Students then simplify, move variable terms to one side, move constants to the other, and isolate the variable using inverse operations.

📚 What You Should Already Know

Students should know how to solve two-step equations, combine like terms, distribute a factor, and perform operations with fractions. They should also understand how inverse operations maintain equality on both sides of an equation.

🚀 What Comes Next

Students will continue solving more complex equations involving distribution, multiple fractional terms, and multi-step reasoning. These strategies lead into solving inequalities, systems of equations, and algebraic applications.

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