Lesson Description
This lesson introduces two-step equations, which require applying two inverse operations to isolate a variable. Students will practice following the correct order of operations and maintaining equality while solving algebraic equations.
Learning Objectives
- Solve two-step equations using inverse operations.
- Apply order of operations when solving equations.
- Verify solutions by substitution.
Topics Covered
- Combining inverse operations
- Order of operations in equations
- Checking algebraic solutions
Key Terms
- Two-Step Equation: An equation requiring two operations to isolate the variable.
- Isolate: To get the variable alone on one side of the equation.
- Balance: Maintaining equality by performing the same operation on both sides.
Lesson Examples
Example 1: Addition and Division
- Solve: x / 3 + 4 = 10
- Subtract 4 from both sides: x / 3 = 6
- Multiply both sides by 3: x = 18
Example 2: Multiplication and Subtraction
- Solve: 5x - 7 = 18
- Add 7 to both sides: 5x = 25
- Divide both sides by 5: x = 5
Practice Problems
- x / 4 + 3 = 11
- 6x - 8 = 28
- 2x + 9 = 19
- x / 5 - 2 = 6
Tips & Common Mistakes
- Undo addition or subtraction before multiplication or division when appropriate.
- Always perform operations in reverse order from how they appear.
- Double-check your solution by substituting back into the original equation.
Summary
Two-step equations require performing two inverse operations to isolate the variable. By carefully applying order of operations and maintaining equation balance, students can solve more complex algebraic expressions.
Challenge Problems
- 3x + 11 = 32
- x / 6 - 5 = 7
- 8x - 4 = 60