Equation Solver
How to Use This Solver
Type your linear equation into the input field using x as your variable. Use standard notation: 2x + 3 = 11, or 5x - 4 = 3x + 8. Press Solve and the tool will show you the answer with every step written out. You can also enter equations with parentheses like 3(x + 2) = 18.
What a Linear Equation Is
A linear equation has exactly one variable, and that variable has an exponent of 1 (meaning it is just x, not x squared or x cubed). The word "linear" means the equation describes a straight line when graphed.
Think of an equation as a balance scale. Both sides must stay equal. Whatever you do to one side, you must do the same to the other side. That is the fundamental rule that lets you solve for x.
The Four Steps to Solve
- Simplify both sides. Distribute brackets and combine like terms on each side.
- Move variable terms to one side. Add or subtract to get all x terms on the left.
- Move constants to the other side. Add or subtract numbers to isolate the variable term.
- Divide to isolate x. Divide both sides by the coefficient of x.
Worked Examples
| Equation | Steps | Answer |
|---|---|---|
| 2x + 3 = 11 | Subtract 3: 2x = 8. Divide by 2. | x = 4 |
| 5x - 4 = 3x + 8 | Subtract 3x: 2x - 4 = 8. Add 4: 2x = 12. Divide by 2. | x = 6 |
| 3(x + 2) = 18 | Distribute: 3x + 6 = 18. Subtract 6: 3x = 12. Divide by 3. | x = 4 |
Checking Your Answer
After solving, plug your value back into the original equation. Replace x with your answer and calculate both sides. If both sides give the same number, your answer is correct.
Common Mistakes to Avoid
- Sign errors when moving terms. Subtracting from one side means adding to the other, not subtracting from both.
- Forgetting to distribute when there are brackets. 3(x + 2) is 3x + 6, not 3x + 2.
- Dividing only one term on a side instead of the whole expression. When you divide, both terms on that side must be divided.
- Not checking the answer. A simple substitution confirms whether you got it right or made an error somewhere.