Solving Linear Equations in One Variable

Linear equations are fundamental in mathematics and have wide applications in various fields. They provide a simple yet powerful way to solve real-world problems.

In this article, we will discuss how to solve linear equations in one variable.

What is a Linear Equation?

A linear equation is a mathematical expression that represents a straight line on a graph.

It is written as ax + b = c, where a, b, and c are constants, and x is the variable.

The goal is to find the value of x that satisfies the equation.

For example,

• 2x = 1
• 33x-1 = 0
• 6x+9 = -11

Standard Form of Linear Equations in One Variable

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

a x + b = 0

Where,

• ‘a’ and ‘b’ are real numbers.
• Both ‘a’ and ‘b’ are not equal to zero.

Types of Linear Equations

There are three types of linear equations.

Simple Linear Equation

These equations involve only one variable.

For eaxmple,

2x + 3 = 7

Two-Step Linear Equation

These require two steps to isolate the variable.

For example,

2x – 5 = 9

Multi-Step Linear Equation

These involve more complex operations.

For example,

3(x + 2) – 4 = 7

Also Read About Systems of Linear Equations

Solving Linear Equations Step by Step

Addition and Subtraction Method

To solve linear equations, we can use the addition and subtraction method. The steps are as follows:

1. Isolate the variable term on one side of the equation by adding or subtracting terms.
2. Perform the same operation on both sides to maintain the equation’s balance.
3. Simplify the equation to obtain the variable’s value.

Multiplication and Division Method

Another method for solving linear equations is multiplication and division. Here’s how it works:

1. Isolate the variable by multiplying or dividing both sides of the equation.
2. Perform the same operation on both sides to keep the equation equal.
3. Simplify and find the value of the variable.

Example

Example 1

2x + 3 = 9

Step 1: Subtract 3 from both sides to isolate the variable:

2x + 3 – 3 = 9 – 3

2x = 6

Step 2: Divide both sides by 2 to solve for ‘x’:

2x / 2 = 6 / 2

x = 3

So, the solution to the equation is x = 3.

Example 2

4x – 7 = 13

Step 1: Add 7 to both sides to isolate the variable:

4x – 7 + 7 = 13 + 7

4x = 20

Step 2: Divide both sides by 4 to solve for ‘x’:

4x / 4 = 20 / 4

x = 5

So, the solution to the equation is x = 5.

Solving linear equations in one variable is a valuable skill with wide-ranging applications.