Algebra 101 - Unit 2

Solving Two-Step Equations

Two-step equations are algebraic equations that require **two inverse operations** to solve for the variable. Typically, these involve a combination of addition or subtraction **and** multiplication or division.

1. Steps to Solve Two-Step Equations

1. Identify the variable and the two operations applied to it.
2. Undo the operations in reverse order using inverse operations:
   • Start with addition or subtraction.
   • Then handle multiplication or division.
3. Perform the same operations on both sides of the equation.
4. Check your solution by substituting it back into the original equation.

2. Examples

Example 1: Solve 2x + 3 = 11

1. Subtract 3 from both sides: 2x + 3 - 3 = 11 - 3 → 2x = 8
2. Divide both sides by 2: 2x / 2 = 8 / 2 → x = 4

Example 2: Solve 3y - 5 = 10

1. Add 5 to both sides: 3y - 5 + 5 = 10 + 5 → 3y = 15
2. Divide both sides by 3: 3y / 3 = 15 / 3 → y = 5

Example 3: Solve (1/2)x + 4 = 9

1. Subtract 4 from both sides: (1/2)x + 4 - 4 = 9 - 4 → (1/2)x = 5
2. Multiply both sides by 2: (1/2)x × 2 = 5 × 2 → x = 10

3. Tips for Success

• Always undo addition/subtraction before multiplication/division when solving.
• Perform the same operation on both sides to keep the equation balanced.
• Check your solution by plugging it back into the original equation.
• Work step by step; don’t skip operations.

Mastering two-step equations prepares you for multi-step equations, equations with variables on both sides, and more complex algebra problems.