How to Solve Linear Equations
To solve a linear equation, simplify both sides, collect the variable on one side, and divide by its coefficient. Check by substituting the result.
What is a linear equation?
A linear equation in one variable can be written as ax + b = c with a ≠ 0. The graph of y = ax + b is a line, and solving ax + b = 0 finds where that line crosses the x-axis.
When to use this method
Use inverse operations whenever the unknown appears to the first power only. If you see x², start with quadratic methods instead.
Step-by-step method
- Distribute and combine like terms on each side.
- Move variable terms to one side and constants to the other.
- Divide by the coefficient of the variable.
- Substitute the answer into the original equation.
Example
2x + 5 = 17
- 2x = 17 − 5 = 12
- x = 12 / 2 = 6
- Check: 2(6)+5 = 17
Answer: x = 6
Interactive example
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Example problems
Common mistakes
Only changing one side
Whatever you do to the left, do to the right.
Dividing a sum incorrectly
(2x + 4)/2 is x + 2, not x + 4.
Related formulas
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Frequently asked questions
What if the variable is on both sides?
Subtract one of the variable terms from both sides so x appears only once, then continue.