Linear equation calculator

A linear equation is one in which the unknown x appears only to the first power: no x² and no x in a denominator. Any such equation can be rearranged into the form ax + b = c.

Watch the signs. From 2x − 7 = 3, enter b = −7, not 7. And if x also appears on the right-hand side, move it to the left first: 5x + 1 = 2x + 10 is the same as 3x + 1 = 10.

How it works

From the form ax + b = c, the root is found with one formula:

$$x=\frac{c-b}{a}$$

We rearrange the equation so that x is left on its own. For the default equation 3x + 5 = 20, first subtract 5 and then divide by 3:

$$\begin{array}{rcl}3x+5& =& 20/-5\\ 3x& =& 15/÷3\\ x& =& 5\end{array}$$

Check: 3 · 5 + 5 = 20. It works.

You can only divide by a non-zero number, so a = 0 is a special case. The equation 0 · x + 5 = 5 holds for any x, whereas 0 · x + 5 = 20 holds for none. You can find more examples, including ones with fractions and brackets, in the article on linear equations.