Solving Linear Equation in One Variable Class 8 Maths – Linear Equation Examples

Solving Linear Equation in One Variable Class 8 Maths – Linear Equation Examples

Linear Equation in One variable is the equation of the form:
ax+b=0
Here, are integers and is a variable and the degree of the variable in the equation is one. (Degree of the variable is the highest power of the variable.)

Constant: A constant is a symbol that has a fixed numerical value. For example: In the expression:
, In the 2x+7=0, the constant term is 7.

Variable: A quantity is a symbol that can take various numerical values. For example: In the expression:
,5x+9=2 the variable is x .
Both numbers and variables can be transposed from one side of the equality to the other side.

Algebraic operation: It is any operations of arithmetic, which include addition, subtraction, multiplication, division. Consider. 3x+1 Here, + is an algebraic operation.

Term: A term is either a single number or variable or numbers and variables multiplied together.
For example, 4x+9
Here, 4x, 9 are the terms.

Algebraic Expression: It is an expression made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. They are also termed as algebraic equations.A statement of equality of two algebraic expressions involves one or more variables. 5x+9 For example is an algebraic expression.

Algebraic Equation: An algebraic expression that contains the sign of equality.An algebraic equation is an equality involving variables. It says that the value of the expression on one side of the sign of equality is equal to the value of the expression on the other side of equality. For example, 5x+2=6 is an algebraic equation.

In linear equations, the expressions which form the equation contain only one variable. A linear equation may have a solution in the form of any rational number.An equation may have linear expressions on both sides. Linear equations can be used to solve different problems regarding numbers, ages, perimeters, combination of currency notes, and so on.
Examples of Linear Equations in one variable:

• 3y+2=9 is a linear equation in one variable such that the degree of the equation is 1.
• 4z+3=2 is a linear equation in one variable such that the degree of the equation is 1.
• 3x^2+7=0 is not a linear equation in one variable as the degree is 2.
• 4x+6y=1 is not a linear equation in one variable as it contains two variables

There are two methods for solving Linear Equation in one variable:

Balancing Method: In this method, the same number is added or subtracted from both sides without disturbing the equation to find the solution.

For example: Find the solution of 5x-10=15
5x-10=15
5x-10+10=15+10
5x=25
x=25/5
=5
Add 10 on both sides.

Transposing Method: In this method, constants or variables are transposed or transferred from one side to another until we get the solution of the equation. When the terms are transposed, the sign of the term changes.

For example: Find the solution of 6x-2=4
6x-2=4
Transpose 2 from L.H.S to R.H.S
6x=4+2
⇒6x=6
x=6/6=1
STEP-WISE PROCEDURE ON SOLVING LINEAR EQUATION IN ONE VARIABLE:

• Read the given word problem carefully
• Identify the given information and what is required.
• Use letters x, y, z, etc. to represent the unknown quantity.
• In the problem, transform the statements into mathematical statements.
• Form the linear equation as per the given conditions of the problem.
• Solve the equation by the usual method.
• Check the solution for its validity. Reject if the solution is invalid.

LINEAR EQUATIONS EXAMPLES: Questions Based on Linear Equation in One Variable – Class 8:

Ques 1: The perimeter of a rectangular swimming pool is 160 m. Its length is 5 m more than twice its breadth. Find the dimensions of the pool.

Solution:

Let the breadth of the swimming pool be m
As the length of the swimming pool is 5 m more than twice its breadth,
Length of the swimming pool 2x+5

Area of the swimming pool = 2(Length+ Breadth)
=2(2x+5+x)
=2(3x+5)
=6x+10

Also,
The perimeter of a rectangular swimming pool 160 m

So,
6x+10=160
⇒6x=160-10=150
⇒6x=150
⇒x=150/6=25

So,
The breadth of the swimming pool=25 m
Length of the swimming pool=2(25)+5=55 m

Ques 2: Solve:4x+9=10

Solution: 4x+9=10
Transpose 9 from L.H.S to R.H.S
4x=10-9
⇒4x=1
⇒x=1/4

Ques 3: Solve the linear equation
x/2-1/5=2x/5+2/5

Solution:
x/2-1/5=2x/5+2/5
⇒x/2-2x/5=2/5+1/5
⇒(5x-4x)/10=3/5
⇒x/10=3/5
⇒x=(3×10)/5=6

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