# Algebra

Mathematicians developed a type of equation containing variables which could be multiplied together and divided into equal groups to create equal values. These values are called the coefficients of a particular equation. The combination of equations makes up an algebraic expression. In algebra, variables or unknown values are represented by letters or pronumerals, which might vary based on the situation.

Formulas, which are equations that connect two or more variables, can also be created using algebra. Being able to replace into and rearrange formulas is crucial because many individuals use them in their daily work.

## Algebraic Notation

"Algebraic Notation" or "x, y, z notation" is the most widely accepted method of representing algebraic expressions. It is a standardized way of writing algebraic expressions that makes them easier to read, comprehend and remember than their handwritten equivalents. Some people use it for two reasons:

Variables are also often represented as letters, numbers or symbols. For example, x and y in a variable x+y might represent the value of variable x (or, more simply, its numerical value) plus variable y (or more accurately its algebraic equivalent). Variables can be thought of as mathematical function names and are used most commonly in equations to represent values that dont change during the problems solution.

· x^2 + 3x it is an expression

· x^2 + 3x = 8 it is an equation

· x^2 + 3x > 8 it is an inequality or inequation

## Algebraic Substitution

"Algebraic Substitution" is the process of using algebraic equations to solve a problem that has variables. With algebraic substitution, the variables must be placed in place of numbers or letters in an algebraic expression. The value of the variable will always equal the coefficient (number or letter) multiplied by whatever value is placed in its place.

*Question: What is the method that is applied in algebraic substitution?*

*Answer: To know how to solve numerical and examples related to algebraic substitution, visithttps://youtube.com/channel/UCoqI7C9rI2UbFPITF2bPgnQ*

## Linear Equations

Equations that have the form ax + b = 0 where x is the unknown variable and a, b are constants are known as linear equations.

In the case of an equation such as "2x + 3 = 6," it is easy to recognize that the unknown variable is being multiplied by the constant.

**Steps To Solve Linear Equations:**

· Decide how the expression containing the unknown has been ‘built up’.

· Perform inverse operations on both sides of the equation to ‘undo’ how the equation is ‘built up’. In this way we isolate the unknown.

· Check your solution by substitution.

The Distributive Law

It states that: a (b + c) = ab + bc

One rule that must be followed when using the distributive law is that when distributing two times or more, no symbols are to be repeated.

To Solve Using Distributive Law:

If the unknown is present on both sides of the equation, we expand any brackets, group like terms, transfer the unknown to one side, the remaining terms to the other, simplify the equation, and then solve it.

## Rational Equations

Equations using fractions are known as rational equations. The numerators are then equated once all fractions in the equation are written with the same lowest common denominator (LCD).

The LCD of two fractions is the least common multiple (LCM) of the denominators. To find the LCD of two or more numbers, we multiply all of them together. To find the LCM for three or more numbers we multiply together every possible pair and then add up those products.

## Linear Inequations

Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. The goal is to use one or more equations to determine the value of the unknown variable.

Points to Ponder:

· If we add or subtract the same number to both sides, the inequation sign is maintained. For example, if 5 > 3, then 5 + 2 > 3 + 2.

· If we multiply or divide both sides by a positive number, the inequation sign is maintained. For example, if 5 > 3, then 5 x 2 > 3 x 2.

· If we multiply or divide both sides by a negative number, the inequation sign is reversed.

· For example, if 5 > 3, then 5 x -1 < 3 x -1

· Interchanging the side reverses inequality sign

*Question: How can we solve problems of inequality? Are there any specific rules in solving them?*

*Answer: The above points must be taken into consideration while solving the linear equation. To know more about the rules, visithttps://youtube.com/channel/UCoqI7C9rI2UbFPITF2bPgnQ.*