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The First Order Equations With One Variable Calculator will calculate:

- The solution (root) of first-order equations with one variable.

Solution = |

First-Order Equations with One Variable Formula and Calculations |
---|

x = -b/ax = - /x = |

First Order Equations With One Variable Calculator Input Values |

Coefficient (a) = |

Constant (b) = |

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each first order equations with one variable calculation, the First Order Equations With One Variable Calculator will automatically calculate the results and update the formula elements with each element of the first order equations with one variable calculation. You can then email or print this first order equations with one variable calculation as required for later use.

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An equation is a mathematical statement consisting of an equal symbol between two algebraic expressions (open sentences) that have the same value. When combined, these two equal open sentences form a single closed sentence. The difference between closed sentences and equations is that closed sentences may be either true or false while equations are supposed to be always true.

Like in algebraic expressions, every equation contains variables, coefficients and constants.

Variables are unknown numbers expressed by means of letters, for example, x, y, z, a, b, c, m, n, etc. The ultimate goal when dealing with an equation is to calculate the value of its variables.

Coefficients are numbers that multiply (or divide) variables and that precede them. It is a norm that if during calculations a coefficient appears after the variable, the equation is rearranged so that all coefficient precede their corresponding variable.

For example, in the equation 3x - 2y = 6, we have two coefficients: 3 and -2 and they are followed by their corresponding variables: namely x and y.

Constants are "free" numbers that are not associated with any variable. They usually appear after the equal sign (giving the value of the equation), but we may see constants appearing in the side that contains variables as well, especially in the original form of equations (before making any operation). In the above equation, the constant is 6.

Any part of the equation containing the product of a coefficient and one or more variables (they may also be in a certain power) is called a term. Equation terms are separated from each other by 'plus' or 'minus' symbols. This means addition and subtraction act as separators of any equation terms, which on the other hand bear the sign preceding them. In addition, the constant also represents a separate term in an equation.

The simplest type of equation is the first-order equation with one variable. As the name implies, such equations have a single variable, which is in the first power. The terms 'first order' or 'first degree' are used to describe equations where variables appear in the first power only. For example, 2x - 4 = 0 is a first-order equation with one variable, as there is a single variable (x) in the equation and this variable is in the first power (x^{1} = x).

Solving a first-order equation with one variable means calculating the value of its variable. In math language, this process is called "finding the root of the equation".

The general form of first-order equations with one variable is

ax + b = 0

where x is the variable, a is the coefficient and b is the constant of the equation. The first thing to do when solving such equations is to isolate the variable. Thus, we have

ax + b = 0

ax = -b

ax = -b

Dividing both sides by a yields

ax/a = -*b**/**a*

x = -*b**/**a*

x = -

For example, in the equation 3x - 4 = 0, we have a = 3 and b = -4. Thus,

x = -*b**/**a*

= -*-4**/**3*

=*4**/**3*

= -

=

The following Math tutorials are provided within the Equations section of our Free Math Tutorials. Each Equations tutorial includes detailed Equations formula and example of how to calculate and resolve specific Equations questions and problems. At the end of each Equations tutorial you will find Equations revision questions with a hidden answer that reveal when clicked. This allows you to learn about Equations and test your knowledge of Math by answering the revision questions on Equations.

- 9.1 - Variables, Coefficients and Constants. First Order Equations with One Variable
- 9.2 - Word Problems Involving Equations
- 9.3 - Identities
- 9.4 - Iterative Methods for Solving Equations
- 9.5 - Quadratic Equations
- 9.6 - The Quadratic Formula
- 9.7 - Systems of Linear Equations. Methods for Solving Them.
- 9.8 - Relationship between Equations in Linear Systems. Systems of Equations with One Linear and One Quadratic Equation