📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- Isolate the variable by undoing operations in the reverse order.
- When an expression is divided by a number, multiply both sides by that denominator to clear the fraction.
- Use inverse operations such as addition, subtraction, multiplication, and division.
- Keep the equation balanced by performing the same operation on both sides.
- Check the solution by substituting it into the original equation.
✏️ Worked Examples — Solving and Checking Multi-Step Equations
🧠 Math Vocabulary
- Inverse operations: Operations that undo one another, such as addition and subtraction.
- Isolate: To get the variable alone on one side of an equation.
- Denominator: The number below the fraction bar that shows the divisor.
- Equivalent equations: Equations that have the same solution.
- Substitution: Replacing a variable with a value to check whether a solution is correct.
💡 Main Idea
This lesson focuses on solving linear equations that involve fractions and multi-step reasoning. Students simplify each equation step by step, use inverse operations to isolate the variable, and check the solution by substituting it into the original equation. Each operation must be performed on both sides to keep the equation balanced.
📚 What You Should Already Know
Before this lesson, students should understand one-step and two-step equations, integer operations, fraction operations, and the meaning of equality. Students should also know that solving an equation means finding a value that makes both sides equal.
🚀 What Comes Next
Next, students can extend these strategies to equations with variables on both sides, equations requiring distribution or combining like terms, and real-world problems. These skills also prepare students to solve multi-step inequalities and more advanced algebraic equations.
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