# Beta version

BETA TEST VERSION OF THIS ITEM

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

# Input equation, which you want to solve

Parameters of the ax + b = 0 equation | ||

Coefficient a (just before x) | ||

Free parameter b |

# The solution of your equation

The equation you entered | ||

Show source$2\cdot x+5 = 0$ | ||

The solution of the equation | ||

Show source$x = \frac{-5}{2}$ |

# The solution step-by-step

I. We subtract free term (b) from both sides.

$2\cdot x+\cancel{5}-{\color{#ffff33}{\cancel{5}}} = 0 -{\color{#ffff33}{5}}$$2\cdot x = -5$

II. We divide both sides by coefficient standing just before x (a).

$\frac{\cancel{2}\cdot x}{{\color{#ffff33}{\cancel{2}}}} = \frac{-5}{{\color{#ffff33}{2}}}$$\begin{aligned}x& = \frac{-5}{2}\end{aligned}$

$2\cdot x+\cancel{5}-{\color{#ffff33}{\cancel{5}}} = 0 -{\color{#ffff33}{5}}$$2\cdot x = -5$

II. We divide both sides by coefficient standing just before x (a).

$\frac{\cancel{2}\cdot x}{{\color{#ffff33}{\cancel{2}}}} = \frac{-5}{{\color{#ffff33}{2}}}$$\begin{aligned}x& = \frac{-5}{2}\end{aligned}$

# Some facts

**Linear equation**is an equation that can be presented in the form:

$ax + b = 0$where:

**a**,**b**- fixed parameters, these are numbers which**we know**,

**x**-**unknown**variable, this is the number we're**searching for**.

- To solve the equation, we need to find a number that, after
**inserting in the place of x**, will make the equation true. Then we say that the number**x meets the equation**or**x is the solution**of the equation. - When we're solving the linear equation, we're trying to get to the situation where the
**unknown is on the left**side, and the**right side**contains only**known numbers**. - The equation can be freely transformed by performing the
**same operations on both sides**e.g. dividing both sides by the same number. - If we have a linear equation in the form $ax + b = 0$, we can find a solution by following steps below:

- 1. We subtract the number b from both sides:

$ax + b - b = 0 - b$then we get:

$ax = -b$ - 2. We divide both sides by the number standing at x (a):

$\frac{ax}{a} = -\frac{b}{a}$then the number a on the left side can be cancelled:

$\frac{\cancel{a}x}{\cancel{a}} = -\frac{b}{a}$ - 3. We get a solution:

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

- 1. We subtract the number b from both sides:
- Linear equation is also called the
**first degree equation**. The name comes from the fact that in the linear equation an unknown x exists in**the first power**. - You can find more about different types of equations by visiting our other calculator: Equation types.

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