Algebra 101 - Unit 2

Solving Multi-Step Equations

Multi-step equations are algebraic equations that require more than two operations to solve for the variable. They often include a combination of **parentheses, like terms, addition, subtraction, multiplication, or division**.

1. Steps to Solve Multi-Step Equations

1. Distribute to remove parentheses if needed.
2. Combine like terms on each side of the equation.
3. Use addition or subtraction to move constants or variable terms to one side.
4. Use multiplication or division to isolate the variable.
5. Check your solution by substituting it back into the original equation.

2. Examples

Example 1: Solve 2(x + 3) = 14

1. Distribute: 2x + 6 = 14
2. Subtract 6 from both sides: 2x = 8
3. Divide both sides by 2: x = 4

Example 2: Solve 3x + 5 - 2x = 12

1. Combine like terms: (3x - 2x) + 5 = x + 5 = 12
2. Subtract 5 from both sides: x = 7

Example 3: Solve 4(x - 2) + 3 = 15

1. Distribute: 4x - 8 + 3 = 15 → 4x - 5 = 15
2. Add 5 to both sides: 4x = 20
3. Divide both sides by 4: x = 5

Example 4: Solve 2(x + 3) - 4(x - 1) = 5

1. Distribute: 2x + 6 - 4x + 4 = 5
2. Combine like terms: (2x - 4x) + (6 + 4) = -2x + 10 = 5
3. Subtract 10 from both sides: -2x = -5
4. Divide both sides by -2: x = 5/2

3. Tips for Success

• Always simplify parentheses using distribution first.
• Combine like terms carefully before moving terms across the equals sign.
• Undo addition/subtraction before multiplication/division when isolating the variable.
• Check your solution by substituting it back into the original equation.
• Take it step by step; do not try to combine too many operations at once.

Mastering multi-step equations prepares you for equations with variables on both sides, fractions, and more advanced algebra topics.