# 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 !

# Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

# Input equation, which you want to solve#

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

Coefficient a (just before x) | ||

Free parameter b | ||

Unknown variable (the variable, which we're searching for) |

# The solution of your equation#

The equation you entered | ||

Show source$2~x+5 = 0$ | ||

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~x+\cancel{5}-{\color{#ffff33}{\cancel{5}}} = 0 -{\color{#ffff33}{5}}$$2~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~x+\cancel{5}-{\color{#ffff33}{\cancel{5}}} = 0 -{\color{#ffff33}{5}}$$2~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):

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

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

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

- 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.

# See also#

If you are interested in solving mathematical equations, check out our other calculators:

- Linear equation solver - see how to solve a
**linear equation**in the form $ax + b = 0$ step by step, - Quadratic equation solver - see how to solve
**quadratic equation**in the form $ax ^ 2 + bx + c = 0$ using the so-called delta scheme, - General equation solver - if you don't know which solving method should be applied to your equation, just give us the left and right side and we will try to solve it for you.

# Tags and links to this website#

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