What Is a Linear Equation?
A linear equation (or first-degree equation) is an equality involving an unknown raised to the power of 1. Its general form is ax + b = c, where a ≠ 0.
General form: ax + b = c Solving: ax = c − b x = (c − b) ÷ a Example: 3x + 5 = 14 3x = 14 − 5 = 9 x = 9 ÷ 3 = 3
Equations with variables on both sides
Form: ax + b = cx + d Move the x terms to one side: ax − cx = d − b (a − c)x = d − b x = (d − b) ÷ (a − c) [if a ≠ c] Example: 5x − 1 = 2x + 8 5x − 2x = 8 + 1 3x = 9 x = 3
Special cases
- a = 0 and b = c: identity (0 = 0) → infinite solutions
- a = 0 and b ≠ c: contradiction (3 = 5) → no solution
Frequently asked questions
What is an unknown?
It is the letter (usually x) that represents the unknown value we want to find. The equation is a "riddle" — finding x is the answer.
How do I check if x is correct?
Substitute the value you found back into the original equation. Both sides must be equal. E.g., x=3 in 3x+5=14: 3(3)+5=14 → 9+5=14 ✓.
What if x appears in a denominator?
Multiply both sides by the denominator to clear the fraction. Example: x/2 + 1 = 5 → multiply by 2: x + 2 = 10 → x = 8.
Can a linear equation have two solutions?
No. A linear equation always has exactly one solution (except for the impossible or identity cases). Two distinct solutions only appear in quadratic equations.