Equations with variables on both sides

Math

Definition

These are equations where the variable appears on both the left and right sides. To solve, collect all variable terms on one side and all constants on the other by using inverse operations.

How It Works

  1. Use the distributive property if needed to clear parentheses
  2. Move all variable terms to one side by adding or subtracting
  3. Move all constant terms to the other side
  4. Combine like terms and solve for the variable
  5. Check your solution by substituting back

Examples

  • 5x + 3 = 2x + 12 → 3x = 9 → x = 3
  • 4(x - 1) = 2x + 6 → 4x - 4 = 2x + 6 → x = 5
  • Comparing two phone plans: 30 + 0.10m = 50 + 0.05m

Related Terms

Multi-step equations Combining like terms Distributive property

Study This Concept

Practice equations with variables on both sides with free review games in these units:

Algebra 1 Unit 2: Solving Linear Equations