Linear Equations in One Variable

The general form of linear equation  jx + k = 0. Here j and k are two integers and the solution of x can be only one. For Example, 8x + 7 = 10 is an equation that is linear and has only a single variable in it.  The only solution to this equation would be x = ⅜. In the case of linear equation in two variables, then there will be two solutions since it has two variables. This linear equations formula list reduces your time in searching for these formulas. This list ensures that it will help the students and they do not miss any formula while preparing for competitive exams or board exams. In this worksheet, you will get to work on linear equation in one variable definition, real life examples of linear equations in one variable, word problems, solution, formulas, and worksheet.

What is Linear Equation in One Variable?

When you have a variable of a maximum of one order in an equation, then it is known as a linear equation in one variable. The linear equation is usually expressed in the form of jx + k = 0. Here j and k are two integers and the solution of x can be only one. For Example, 5x + 6 = 10 is an equation that is linear and has only a single variable in it.  The only solution to this equation would be x = ⅘.

Some more examples are: 

  • 52x + 67 = 98

  • 13x - 92 = 139

  • 34x +71 = 88

  • 27x - 9 = 81

  • 99x - 999 = 99999

Types of Linear Equations

The linear equations are of three types:

  • linear equations in one variable

  • linear equations in two variables

  • linear equations in three variables

Linear Equation Formula

The standard form of a linear equation is usually expressed in the form of:

 jx + k = 0

 Here,

  •  j and k are two integers 

  • the solution of x can be only one

  • The value of j and k can never be equal to 0.

Solving Linear Equation In Variable

When you have to solve an equation that has always only one solution, then the steps given below are followed.

  • Step 1: Find the LCM. In case any fractions exist, clear them. 

  • Step 2: In this step simplification of both the sides of the equation happens. 

  • Step 3: Here, you will be isolating the variable on one side.

  • Step 4: You will verify the obtained result. 

Linear Equation in One Variable Formula Table

You might have already covered the concept of linear equations in one variable definition in your earlier classes like class 6, class 7, and class 8. In this article, you’ll be studying an advanced version of linear algebra. CBSE Class 11 contains algebra concepts in many chapters - such as the algebra of complex numbers, algebra of real numbers, algebra of an event and algebra of derivative of a function. Sometimes it becomes difficult to remember these formulas. Hence the list of formulas was made to help you. 

The Important Formulas Related to Algebraic Function Are

Important Algebra Formulas For Class 11

Distributive Property

r ( s + t ) = r × s + r × t

Commutative Property of Addition

r + s = s + r

Commutative Property of Multiplication

r × s = s × r

Associative Property of Addition

r + ( s + t ) = ( r + s ) + t

Associative Property of Multiplication

r × ( s × t ) = ( r × s ) × t

Additive Identity Property

r + 0 = r

Multiplicative Identity Property

r × 1 = r

Additive Inverse Property

r + ( − r ) = 0

Multiplicative Inverse Property

r ( 1 / r )=1

Zero Property of Multiplication

r × ( 0 ) = 0 <


Linear Equation in One Variable Problems

Question 1: Solve the following equation: 6x + 9 = 18x - 12

Solution: Shift the vales that have variables on one side. In this step, you will be shifting 6x and 18 x on one side and 9 and 12 on the other. Note that the sign changes when you transfer them from one side to the other. Here, the 6x from the left hand side will be shifted to the right hand side with the 18x and the -12 from the right hand side will shift to left hand side with 9. Once this trader is don with the change od signs, the equation will look something like this, 

6x + 9 = 18x - 12

⇒ 9 = 18x - 12 - 6x

⇒  9 = 12x - 12

Step 2: In this step, you will transfer all the variables on one side of the equation and all the constants on the other side of the equation. In this equation, 12 will divide 21.

⇒  9 = 12x - 12

⇒  9 + 12 = 12x 

⇒  21 = 12x 

Step 3: Now you will have to divide the equation with 12 on both the sides

⇒  21 / 12 = 12x / 12

⇒  21 / 12 = x

Step 4: To verify whether the answer is correct or not, substitute the value of x in the equation which was given to solve. 

6x + 9 = 18x - 12

6 ( 21 / 12 ) + 9 = 18 ( 21 / 12 ) - 12

39 / 2 = 39 / 2

Left hand side value = Right Hand Side Value

Hence Proved. 

Linear Equation Problems

  1. Find the solution n to the equations:

  • n + 3 = 9

  • 8 n + 6 = 5

  • 17n + 31 = 42

  • 4/3n + 68 = 100

  • 145n - 87 = 900

  • 34 - 65n = 326

FAQ (Frequently Asked Questions)

1. What is Linear Equation Definition of One Variable?

When you have a variable of a maximum of one order in an equation, then it is known as a linear equation in one variable. The linear equation is usually expressed in the form of jx + k = 0. Here j and k are two integers and the solution of x can be only one. For Example, 5x + 6 = 10 is an equation that is linear and has only a single variable in it.  The only solution to this equation would be x = ⅘.

2. How to Solve Linear Equations?

When you have to solve an equation that has always only one solution, then the steps given below are followed.

  • Step 1: Find the LCM. In case any fractions exist, clear them. 

  • Step 2: In this step simplification of both the sides of the equation happens. 

  • Step 3: Here, you will be isolating the variable on one side.

  • Step 4: You will verify the obtained result.