Linear Equations in One Variable is a basic equation that can be expressed in the form ax+b=0 in which a, b are integers and x is a variable. Linear Equation in One Variable has a single solution for it. In this article, we have covered everything like Definition, Standard Form of Linear equation in One Variable, How to Solve Linear Equation in One Variable with enough Examples.
See More: Solving Linear Equations
What is meant by Linear Equations in One Variable?
A Linear Equation is a kind of equation in which the degree of each variable in the equation is one. Linear Equations in One Variable has only one Variable in it and has only one solution to it. When we draw it on a graph it appears to be a straight line in the horizontal or vertical direction.
Example of Linear Equation in One Variable 5x+20=45
Standard Form of a Linear Equation in One Variable
The Standard Form of a Linear Equation in One Variable is ax + b = 0 Where a is the coefficient of x and b is the constant term. We need to segregate the coefficient and constant term to get the solution of the linear equation.
How to Solve Linear Equations in One Variable?
Follow the simple steps listed below to solve linear equations in one variable. They are as under
- Initially, place the constant term on one side and the coefficient term on another side by either adding or subtracting on both sides of the equation.
- Simplify or reduce the constant terms
- Isolate the variable on one side by either multiplying or dividing it into both sides of the equation.
- Simplify and note down the answer.
How to Frame Linear Equation in One Variable using Word Problem?
Go through the simple steps and learn how to frame a linear equation in one variable from a given word problem. They are as follows
- First of all, read the given data carefully and make a note of the required quantities separately.
- Mention the unknown quantities as x, y, z
- Convert the problem into a mathematical statement.
- Frame Linear Equation in One Variable using the given conditions in the Problem.
- Solve the Equation for Unknown Quantity.
Linear Equations in One Variable Questions
Example 1.
Solve for x, 2x-6=0?
Solution:
Given Linear Equation in One Variable 2x-6=0
Add 6 on both sides
2x-6+6=0+6
2x=6
x=3
Example 2.
Solve 4m-12=8?
Solution:
Given Linear Equation in One Variable 4m-12=8
4m=8+12
4m=20
m=5
Example 3.
The length of the legs of an isosceles triangle is 5 meters more than its base. If the Perimeter of the triangle is 40 meters, find the lengths of the sides of the triangle?
Solution:
Let us assume the base measures the ‘x’ meter. Hence, each of the legs measure y = (x + 5) meters.
The Perimeter of a triangle is the sum of the three sides.
The equations are formed and solved as follows:
x + 2(x + 5) = 40
x + 2x + 10 = 40
3x + 10 = 40-10
3x = 30
3x = 10
x = 30/3
x = 10
The length of the base is solved as 10 meters. Hence, each of the two legs measures 15 meters.
Example 4.
Fifteen years ago, Mohan’s age was one-fourth of what it is now. What is Mohan’s present age?
Solution:
We can write the given information by using a linear equation in one variable. Let Mohan’s present age be x years. Fifteen years ago, Mohan’s age was (x-15) years. According to the given information, x – 15= x/4
4(x – 15)= x
4x – 60= x
4x – x= 60
3x= 60
x= 60/3
x= 20
Therefore the present age of Mohan is 20 years.