What are Linear Equations? How to Solve Linear Equations in One Variable


Linear Equations is one of those topics which has wide applications in other fields of mathematics such as calculus, probability, etc. Its uses are also quite evident in subjects like physics, biology, finance, economics, sociology, and other engineering fields. With such wide applications in various fields, Linear Equations becomes one of the most important topics. Solving Linear Equations can boost the logical and reasoning abilities of a student. It can also help in the development of critical thinking. In this blog, we will understand what a linear equation is. We will also solve linear equations in one variable and solve each step in detail.

What is a Linear Equation?

An equation in the algebraic form of ax+b=c, which involves a constant and a first-order term, is known as a linear equation. Here a is the slope of the linear equation, and b is the y-intercept.

Linear Equation in One Variable

A linear equation in one variable consists of only one variable in the algebraic equation. For example, in the equation ax+b=c. X is the only variable, whereas a,b, and c are constants. Some examples of linear equations in one variable are: 2x+2=10, 90+3x= 150.

Solving Linear Equations in One Variable

Here is a step by step guide on solving Linear Equations with one variable. These equations can be used to solve a variety of problems.

Step 1: If the linear equation has any fraction, we need to use the least common denomination in order to clear the fraction present in the linear equation. We can simply multiply both sides by the least common denominator.

Step2: Step 2 is the simplification of the equation. This is done to clear parentheses and combine the like terms.

Step3: Now, all the terms with variables can be kept on one side, and constants need to be placed on the other side. The constants have to be added in this step.

Step4: In this step, we need to make the coefficient a one. One can perform the operation and find the value of the variable.

Step5: It is the most important step as it requires you to check the equation. You can simply put the value and check the equation. If the value doesn’t match, you need to revisit the previous steps and see if you have applied the inverse law properly. Make sure you have made proper sign changes and added the constants properly,

These were the simple steps that can help you solve a linear equation in one variable. Regular practice of these equations is necessary so that you can get used to the arithmetic rules which are required to solve a linear equation in one variable. Linear equations in one variable is a very important topic, and it lays a foundation for complex topics like linear equations in two variables. Hence it is important to practice a variety of questions based on this topic. You can provide multiple interactive worksheets by Cuemath, which can help you understand the concept of linear equations in an engaging way. These worksheets have visual simulations that can help students get an in-depth understanding of the topic. These worksheets can make the learning process super fun for the kids.

I hope this blog helped you understand linear equations in one variable. In case of queries, feel free to comment down below.

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