The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

In mathematics, **algebra** is the branch that revolves around solving certain mathematical equations in order to derive unknown quantities. The variables in **algebra** can be used to equate known quantities or constant values to solve for the unknown value that is required as the answer. We usually denote this unknown variable with ‘x’ or ‘y’ conventionally.

We use algebraic formulas in our daily lives to find out the distance, volume of containers and also to find out prices of goods and commodities in large numbers. **Algebra** is helpful in defining a mathematical equation that can then form relationships with other values and entities to ultimately give you a solvable equation.

Some of the main topics in the NCERT syllabus for **algebra** include coming under **algebra** exponents, simplification, linear equations, linear inequalities, quadratic equations, polynomials, to name a few. As we know, **algebra** is the branch of mathematics that is based on unknown values called variables. This integral concept of **algebra** is expressed via equations that follow the various rules to perform arithmetic operations in order to solve for the unknown variable.

Addition and subtraction of two or more algebraic expressions is relatively easy. It is quite similar to the arithmetic formats. It is also easy to **generate algebraic expressions** in the same way.

For addition, follow the steps mentioned below:

- Write down the algebraic expressions given to you one below the other wherein the variables that are matching in the two equations are written directly below each other.
- Then we merely add the constant coefficients to each other arithmetically to arrive at the value.
- We then write the answer with the variable and the new value of the constant after addition to arrive at the result required.

**Example:**

Add 5x – 12y and y – 3x.

**Solution:**

For adding these 2 given algebraic expressions we write as follows:

5x – 12y

-3x + y

_______

2x – 11y (Answer)

Subtraction is a little different from the basic arithmetic subtraction. The steps for the same are mentioned below:

- Write down the terms containing the same variables below one another.
- Note the subtracted value and the expression from which the values are to be subtracted. This order of expressions is integral.
- Then merely change the arithmetical operator associated with each term from the expression to be subtracted.
- Then perform mere arithmetic subtraction to arrive at the answer you require.

**Example:**

Subtract x + y from 15y – 4x

**Solution:**

Write down the two given equations as follows:

-4x +15y

+x + y

(-) (-)

________

-5x + 14y (Answer)

Any algebraic expression that is written in the form of an equation in the generic form of ax + b =0 is called a simple linear equation or a linear equation in one variable. In this case, the variable is ‘x’ and the coefficient associated with this variable is ‘a’ which is usually a numerical value. This form of a linear equation in one variable has only one possible solution.

The standard form of **simple** **linear equations in one **variable is represented as:

ax + b = 0

Where ‘a’ and ‘b’ can be any real number which is not equal to zero.

For solving an equation having only one variable, the following basic steps are required to be closely followed:

- Take an LCM of both sides if there are any decimals or fractions in the expression given.
- Simplify both sides of the equation, change the arithmetical operator when moving from one side to the other.
- Isolate the variable to express in the form of ax + b =0 and then solve for x.

Here are a few **Problems based on simple equations**:

Example 1:

Solve for x: 13x + 39 = 0

Solution:

To simplify the given equation we do it as follows:

> 13x = -39

> x = -39/13

Thus, x from the above equation is equal to -3.

Example 2:

Solve for x: 10x + 12 = 21 – 3x

Solution:

To solve the given equation we need to write it in the form of ax +b = 0. We do so as follows:

> 10x + 12 = 21 – 3x

> (10x + 3x) + (12 -21) = 0

> 13x – 9 = 0

> 13x = 9

> x = 9/13 which is the required answer.

**Linear inequalities** are certain types of algebraic expressions where any two values are compared to each other using inequality operators such as ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be arithmetical or algebraic or a mix of both.

The main symbols used in inequalities are:

- < (less than)
- > (greater than)
- ≤ (less than or equal to)
- ≥ (greater than or equal to)
- ≠ (not equal to)

In algebra, the idea to solve for acquiring the values for the unknown variables. It contains various topics such as linear equations in one variable, simple linear equations, linear inequalities, addition and subtraction of linear equations, etc. It is one of the most conceptual branches in maths and is easy to grasp if the basic concepts are clear.

**What is algebra in mathematics?**

In mathematics, algebra is the branch that revolves around solving certain mathematical equations in order to derive unknown quantities. The variables in algebra can be used to equate known quantities or constant values to solve for the unknown value that is required as the answer.

**What do you mean by linear equations?**

Any algebraic expression that is written in the form of an equation in the generic form of ax + b =0 is called a simple linear equation or a linear equation in one variable. This form of a linear equation in one variable has only one possible solution.

**What are linear inequalities?**

Linear inequalities are certain types of algebraic expressions where any two values are compared to each other using inequality operators such as ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.

**What are the various types of expressions in algebra?**

There are five main types of algebraic expressions. These are monomial or polynomial equations, exponential equations, trigonometric equations, logarithmic equations and rational equations.

**How to solve a linear equation in one variable?**

For solving a linear equation having only one variable, take an LCM of both sides if there are any decimals or fractions in the expression given. Then, simplify both sides of the equation, change the arithmetical operator when moving from one side to the other. Finally, isolate the variable to express in the form of ax + b =0 and then solve for x.