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Expressions & Equations
Linear Equations in One Variable
A linear equation has variables raised only to the first power. Standard form: ax + b = c Solving multi-step linear equations: 1. Simplify each side (combine like terms) 2. Get all variable terms on one side 3. Get all constants on the other side 4. Divide by the coefficient Special cases: • No solution: Results in a false statement (e.g., 5 = 3) • Infinite solutions: Results in a true statement (e.g., 5 = 5) • One solution: Results in x = some number
Example:
Solve: 3(x + 4) - 2x = 5x - 8 Distribute: 3x + 12 - 2x = 5x - 8 Combine: x + 12 = 5x - 8 Subtract x: 12 = 4x - 8 Add 8: 20 = 4x Divide: x = 5 Check: 3(5+4) - 2(5) = 27 - 10 = 17 5(5) - 8 = 25 - 8 = 17 ✓