Table of contents  
What is Linear Equation in One Variable?  
Solving Linear Equation in One Variable  
Linear Equation in One Variable vs NonLinear Equations  
Solved Examples 
A linear equation in one variable is the basic equation used to represent and solve for an unknown quantity. It can be easily represented graphically and it is always a straight line. The linear equation is an easy way of representing a math statement. Any variable or symbol can be used to represent unknown quantities but generally, a variable 'x' is used to represent the unknown quantity in the linear equation in one variable.
For solving an equation having only one variable, the following steps are followed
Example: Solve 5x – 9 = 3x + 19
Step 1:
Step 2:
Step 3:
Linear Equation in One Variable VS Non Linear Equation
The following points help us in clearly summarizing the concepts involved in linear equations in one variable.
Example 1: Twenty years ago, Mikkel's age was onethird of what it is now. What is Mikkel's present age?
Solution: We can write the given information by using a linear equation in one variable. Let Mikkel's present age be x years. Twenty years ago, Mikkel's age was (x20) years. According to the given information, x  20= x/3
3(x  20)= x
3x  60= x
3x  x= 60
2x= 60
x= 60/2
x= 30
Therefore the present age of Mikkel is 30 years.
Example 2: David worked as a stenographer. In June, he was paid $50 per day. However, $10 per day was deducted for the days he remained absent. He received $900 for the number of days he worked. How many days did he work?
Solution: Let the number of days he worked be x days. Hence, the number of days he did not work will be = 30  x. He was paid $50 for each day he worked and $10 was deducted for each day he did not work. At the end of the month, he received $900. According to the given information, we can form a linear equation in one variable as, 50(x)  10(30  x) = 900
50x  300 + 10x = 900
60x = 900 + 300
x = 1200/60
x= 20
Therefore David worked for 20 days.
Example 3: Find the perimeter of the square whose side length x units is given in the form of an equation as 2x/3 5/6 = 0
Solution: Given, the sidelength of the square is 2x/3 5/6=0. It is in the form of a linear equation in one variable which is x. First, we need to solve this equation to find the value of x.
2x/3 5/6=0
2x/3 5/6 + 5/6=0+ 5/6 (adding 5/6 on both the sides)
2x/3= 5/6
x = 5/6 × 3/2
x = 5/4 units
Hence, the side length of the square is 5/4 units. Now, to find the perimeter of the square, we need to multiply the side length by 4.
The perimeter of a square = 5/4 × 4=5 units.
Therefore the perimeter of the square is 5 units.
Example 4: The length of the legs of an isosceles triangle is 4 meters more than its base. If the Perimeter of the triangle is 44 meters, find the lengths of the sides of the triangle.
Solution: Let us assume the base measures ‘x’ meter. Hence, each of the legs measure y = (x + 4) meters.
The Perimeter of a triangle is the sum of the three sides.
The equations are formed and solved as follows:
x + 2(x + 4) = 44
x + 2x + 8 = 44
3x + 8 = 44
3x = 44 – 8 = 36
3x = 36
x = 36/3
x = 12
The length of the base is solved as 12 meters. Hence, each of the two legs measure 16 meters.
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1. What is a linear equation in one variable? 
2. How do you solve a linear equation in one variable? 
3. What is the solution of a linear equation in one variable? 
4. Can a linear equation in one variable have more than one solution? 
5. How are linear equations in one variable used in reallife situations? 

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