How to Solve Linear Equations: A Simple Step-by-Step Method
A linear equation is one where the variable is only raised to the power of one — no squares, no roots. Almost every one can be solved with the same four steps.
The four-step method
Follow these in order and you will rarely get stuck.
- •Expand any brackets: 2(x + 3) becomes 2x + 6.
- •Collect variable terms on one side, numbers on the other.
- •Combine like terms on each side.
- •Divide by the coefficient of the variable to isolate it.
Variables on both sides
When x appears on both sides, move all the x terms to whichever side keeps the coefficient positive. Example: 5x − 4 = 2x + 11. Subtract 2x from both sides: 3x − 4 = 11. Add 4: 3x = 15. Divide by 3: x = 5.
Always check your answer
Substitute your answer back into the original equation. If both sides come out equal, you are right. This 10-second habit catches almost every arithmetic slip.
Frequently asked questions
What is a linear equation?
An equation where the variable appears only to the first power, such as 3x + 5 = 20. Its graph is a straight line.
How do I handle brackets?
Expand them first by multiplying the term outside into every term inside, then solve as normal.