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:
Add 5x – 12y and y – 3x.
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:
Subtract x + y from 15y – 4x
Write down the two given equations as follows:
+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:
Here are a few Problems based on simple equations:
Solve for x: 13x + 39 = 0
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.
Solve for x: 10x + 12 = 21 – 3x
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:
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.