Скачать или смотреть Solving linear equations

*CORE CONCEPT*
Solving linear equations involves isolating the variable using inverse operations while maintaining balance through the properties of equality.

*TOPICS COVERED*
When to use inverse operations to isolate variables in linear equations (B1)
How to apply properties of equality to maintain balance while solving equations (B1)
How to check solutions by substituting back into the original equation (B1)

*EXAMPLE SENTENCES*
Example 1: 2x + 3 = 11. Subtract 3 from both sides: 2x = 8. Divide by 2: x = 4.
Example 2: 5x - 2 = 18. Add 2 to both sides: 5x = 20. Divide by 5: x = 4.
Example 3: 3(x - 1) = 12. Distribute: 3x - 3 = 12. Add 3 to both sides: 3x = 15. Divide by 3: x = 5.

*GRAMMAR RULES*
Step 1 → Identify the variable to isolate in the equation.
Step 2 → Use inverse operations to move terms to the opposite side.
Step 3 → Simplify and solve for the variable, then check the solution by substituting back.

*COMMON ERRORS*
Wrong: Confusing the operation: Adding instead of subtracting when isolating the variable. → Right: Always use the opposite operation to isolate correctly.
Wrong: Forgetting to divide by the coefficient of the variable. → Right: Perform the same operation on both sides.
Wrong: Not checking the solution by substituting back. → Right: Substitute back to verify the solution.

*STUDENT QUESTIONS*
How do I isolate the variable in a linear equation?
When to use inverse operations in solving equations?
Is my solution correct if I substitute it back?
What's the difference between adding and subtracting in equations?

*KEY CONCEPTS*
Linear equations, inverse operations, properties of equality, solution verification, B1 level.