Linear Equations
The calculator solves the linear equation ax + b = cx + d step by step: moving terms, combining like terms and checking the answer.
Enter the coefficients (an empty field means zero):
x +=x +
The linear equation solver solves equations of the form ax + b = cx + d step by step: it moves the terms, combines like terms, finds x as a fraction and a decimal and checks the answer. The coefficients can be whole, decimal and negative.
How to solve a linear equation
- Move the x terms to one side of the equation and the numbers to the other. A term that moves across the "=" sign changes its sign.
- Combine like terms to get an equation of the form kx = m.
- Divide both sides by the coefficient k.
Example. 5x + 3 = 2x + 12
5x − 2x = 12 − 3
3x = 9
x = 3
Check: 5 · 3 + 3 = 18, 2 · 3 + 12 = 18 ✓
How many solutions a linear equation has
| After simplifying | Solutions | Example |
|---|---|---|
| kx = m, k ≠ 0 | one solution x = m/k | 3x = 9 |
| 0 · x = 0 | any number | 2x + 1 = 2x + 1 |
| 0 · x = m, m ≠ 0 | no solutions | 2x + 1 = 2x + 5 |
If the equation has brackets, expand them first; if it has fractions, multiply both sides by a common denominator, and it will take the form ax + b = cx + d.