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What is a Linear Equation?

A linear equation is an equation where the highest power of the variable is 1. The general form is:

ax + b = 0
  • a — coefficient (a ≠ 0)
  • b — constant term
  • x — unknown variable

Steps to Solve

Any linear equation can be solved by following these steps:

  1. 1Expand brackets and combine like terms
  2. 2Move variable terms to one side and constant terms to the other
  3. 3Divide both sides by the variable's coefficient
  4. 4Check your answer — substitute the value back into the original equation

Why It Matters

Linear equations are one of the most important foundations in mathematics. Understanding them is crucial for several reasons:

  • Over 40% of SAT algebra questions are based on linear equations
  • Used in everyday life for calculating prices, distances, and rates
  • They serve as the foundation for solving more complex equations (quadratic, exponential)
  • Essential skill for analyzing graphs and data tables

Example

Solve the following equation:

3x + 7 = 22
3x + 7 = 22
3x = 22 - 7
3x = 15
x = 5

Check: 3(5) + 7 = 15 + 7 = 22 ✓

Remember

Whatever operation you perform on one side of the equation, you must perform the same operation on the other side. If you add to one side, add to the other. If you divide one side, divide the other.