📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- Use the distributive property to simplify expressions such as \(8(4x-7.5)\).
- Use inverse operations to isolate the variable one step at a time.
- Perform the same operation on both sides to keep the equation balanced.
- When an expression is divided by a number, multiply both sides by the denominator to clear the fraction.
- Check each solution by substituting it into the original equation.
✏️ Worked Examples — Solving Multi-Step Equations
🧠 Math Vocabulary
- Distributive property: Multiplying a factor by every term inside parentheses.
- 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 represents the divisor.
- Substitution: Replacing a variable with a value to determine whether an equation is true.
💡 Main Idea
This lesson focuses on solving multi-step equations involving decimals, distribution, and fractions. Simplify each equation first, then use inverse operations to isolate the variable. When a variable expression is divided by a number, multiplying both sides by the denominator clears the fraction.
📚 What You Should Already Know
Before this lesson, students should understand one-step and two-step equations, inverse operations, the distributive property, decimal operations, and basic fraction operations. Students should also know how to maintain equality by performing the same operation on both sides.
🚀 What Comes Next
Next, students can solve equations with variables on both sides, equations requiring distribution and combining like terms, and equations with fractional coefficients. These strategies also prepare students for solving multi-step inequalities and algebraic word problems.
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