How to Solve Algebraic Equations?


In Mathematics, an algebraic equation is a mathematical statement that shows the equality of two expressions. The algebraic equation is also known as the polynomial equation. The equation generally indicates the relationship between two values or expressions. We know that algebraic expressions consist of variables, constants, and coefficients connected by the different mathematical operators, such as addition, subtraction, multiplication and division. An equation may involve one variable or more than one variable. We are using algebra in our day to day life activities to solve many problems. Now, let us have a brief introduction to algebra.

Introduction to Algebra

Algebra is a study of different mathematical symbols and the rules to manipulate the symbols. It is a branch of mathematics, which helps to represent problems or situations. Algebra is not just a mathematical concept, but it is a skill that everyone uses daily without realising it. Based on the complexity of the algebraic expressions, algebra is classified into different levels, such as pre-algebra, elementary algebra, abstract algebra, universal algebra, etc. Here, we are going to discuss how to solve an algebraic problem with a complete explanation.

Steps to Solve an Algebraic Equation

To solve a simple linear algebraic equation, follow the steps given below:

Step 1: Reduce each side of the given equation by eliminating the parentheses or combining like terms.

Step 2: Use mathematical operations, such as addition or subtraction, to separate the variable term on one side of an equation.

Step 3: The final step is to solve an unknown variable, which can be done with the help of multiplication or division operation.

Now, let’s solve an equation using the steps mentioned above.

Consider an equation, 4x+3x-2 = 12

The first step is to solve this equation, which is done by combining the like terms on the L.H.S. (Left Hand Side) of an equation. 

Thus, the equation becomes:

7x – 2 = 12

In the second step, keep the variable term on the L.H.S. and bring the constant term to the Right-Hand side (R.H.S.) by changing the constant term sign and perform the addition/subtraction operation.

Hence, 7x – 2 = 12 becomes:

7x = 12+2

7x = 14

The final step is to solve for an unknown variable (x). Here, the coefficient of x is 7. So, bring the coefficient of unknown variables to the R.H.S., and perform division operation.

(i.e) x = 14/7 = 2

Hence, the value of an unknown variable, x, is 2, which is the solution of an equation 4x+3x-2=12.

(Note: A solution is a value, which we can put in the place of an unknown variable, such that it makes the equation true).

It is essential to learn how to solve an equation, as many concepts in Mathematics, such as coordinate geometry, calculus, trigonometry, involve the use of algebra. For example, you should be thorough with the concepts of algebra and geometry to learn trigonometry. Since all the ideas are related to each other, it is advised to learn the concepts in-depth to understand the advanced concepts of Mathematics. Suppose you have a good knowledge of Mathematics. In that case, you can solve any problems in your life, as the subject of mathematics improves our logical, mental and reasoning ability. Subscribe to BYJU’S YouTube channel and learn more interesting mathematical concepts quickly by exploring more videos.

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