📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- Equations can have variable terms on both sides of the equal sign.
- Use inverse operations to move the variable terms to one side.
- Move constant terms to the opposite side of the equation.
- Perform the same operation on both sides to keep the equation balanced.
- Check the solution by substituting it into the original equation.
✏️ Worked Examples — Solving Equations with Variables on Both Sides
🧠 Math Vocabulary
- Variable term: A term that contains a variable, such as \(12x\) or \(5x\).
- Constant: A number without a variable, such as \(3\) or \(31\).
- Inverse operations: Operations that undo one another, such as addition and subtraction.
- Isolate: To get the variable alone on one side of the equation.
- Substitution: Replacing a variable with a value to check whether the equation is true.
💡 Main Idea
This lesson focuses on solving equations in which the variable appears on both sides. The key strategy is to move the variable terms to one side and the constants to the other using inverse operations. After simplifying the equation, isolate the variable and check the solution in the original equation.
📚 What You Should Already Know
Before this lesson, students should understand how to solve one-step and two-step equations, use inverse operations, identify like terms, and maintain equality by performing the same operation on both sides.
🚀 What Comes Next
Next, students can solve more complex equations involving the distributive property, combining like terms, fractional coefficients, and special cases with no solution or infinitely many solutions. These skills also prepare students for inequalities and systems of equations.
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