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Basic Algebra

How to Solve Linear Equations (With Examples)

Updated · By the SolverCalc team

Quick answer

Undo operations in reverse order, keep the equation balanced, then check by substituting.

A linear equation has a variable raised only to the first power, such as 3x + 7 = 22. Solving it means finding the value of x that makes both sides equal. The key idea is balance: whatever you do to one side, you must do to the other.

Example 1: a two-step equation

  1. Start with 3x + 7 = 22.
  2. Subtract 7 from both sides: 3x = 15.
  3. Divide both sides by 3: x = 5.
  4. Check: 3 × 5 + 7 = 15 + 7 = 22. ✓

Example 2: variables on both sides

  1. Start with 5x − 4 = 2x + 11.
  2. Subtract 2x from both sides: 3x − 4 = 11.
  3. Add 4 to both sides: 3x = 15.
  4. Divide by 3: x = 5.
  5. Check: left side 5 × 5 − 4 = 21; right side 2 × 5 + 11 = 21. ✓

Example 3: parentheses

  1. Start with 4(x − 2) = 3x + 5.
  2. Distribute the 4: 4x − 8 = 3x + 5.
  3. Subtract 3x from both sides: x − 8 = 5.
  4. Add 8 to both sides: x = 13.
  5. Check: 4(13 − 2) = 4 × 11 = 44 and 3 × 13 + 5 = 44. ✓

A general strategy

  • Clear parentheses using the distributive property.
  • Combine like terms on each side.
  • Move all variable terms to one side and constants to the other.
  • Divide by the coefficient of the variable.
  • Substitute your answer into the original equation to check it.

Checking is the step most students skip, yet it catches nearly every sign error. Use the calculator to evaluate both sides with your value of x—if they match, you are done.

Practice problems

EquationAnswer
6x − 9 = 27x = 6
2(x + 4) = 3x − 1x = 9
x/5 + 2 = 7x = 25