In this chapter, You are going to learn linear equations in one variable, which You already learned some basics in class 7th. So, you already have little knowledge about linear equations. Now in class 8th, you are going to get a little more knowledge about this topic.
Before that have need to know :
What is a linear equation in one variable?
The standard form of the linear equations in one variable is represented as:
ax + b = 0
- ‘ A ’ and ‘ b ’ are the real numbers and the
- Both of these ‘ a ’ and ‘ b ’ are not equal to zero.
Thus, the formula of the linear equation in one variable is ax + b = 0.
For example, 2x+3=8 having a single variable in the linear equation. The output of this equation has only one solution, which is x = 5/2.
Concepts in 8th text book
- Standard form
- Steps for solving
- Word problems
- Practice Questions
Solving an equation having only one variable
A solving an equation having only one variable, the following steps are followed
- Step 1:-Using LCM,
- Step 2: Simplify both sides of the equation.
- Step 3: Isolate the variable.
- Step 4: Verify your answer.
Linear Equations in one variable word problems
Problem: 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 in 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.
Try it, a few practice questions are given below.
- Question 1: Solve ( 10x – 7) = 21
- Question 2: Find the multiples, if the sum of two consecutive multiples of 6 is 68.
- Question 3: Verify that if the x = -3, is a solution of the linear equation 10x + 7 = 13 – 5x.
So, in Linear Equations in One Variable NCERT Maths Class 8th In Chapter 2 you will be getting this type of question where you need to solve them by following the formula. If you follow the basics you can learn it easily.
Most of them ask questions like
How many solutions does a linear equation have in one variable?
Every linear equation in one variable has one and a unique solution. If an equation has two or more variables then it becomes a linear equation in two variables or linear equations in three variables and so on and the number of various solutions as per the count of variables an equation contains.
How easily can you solve any equation having one variable?
First, put the variable on the left-hand side and then numerical values on the right-hand side. Then Change the operators while changing sides of the terms and then solve for the variable.
In this lesson you will have learned more about linear equations. After completing the task,now you have deep knowledge about linear equations. Many things you have learned. We Hope you had fun doing the task .