In this chapter, we study linear expression in one variable only. It is an important topic to build basic knowledge about linear equations. There are 6 exercises in this chapter. The NCERT Solutions for Class 8 Maths Linear Equations in One Variable are prepared and explained by the experts for the students to develop a grip on the topic.
Linear equations help us write a large problem in a simpler way, a problem like the present age of Ram’s mother is 3 times the present age of Ram, after 5 years their ages will add to 65 years. Find their present ages. So how to solve a problem like this, we easily learn in NCERT Class 8 Maths Chapter 2 Linear Equations in One Variable. Before going into detail, we need to understand some basics like what is the difference between “Expressions” and “Equation” in mathematics.
An algebraic expression is a mathematical phrase that contains numbers, variables, and operators. For example- “3x + 7” in which 3 and 7 are numbers, x is variable and ‘+’ sign is the operator.
It is a statement of equality of two expressions it means equations contain “equal to(=)” operator between two expressions. For example 3x + 7 = 0, 3x + 7 = 20 etc.
Now moving onto the actual topic of Chapter 2 Linear Equations in One Variable. What is a linear equation in one variable basically? Let's understand with an example:
Example:- 5 is added to a number gives us 9 find that number, we know its 4 but that not the reason why we asked this question. We can represent this problem in a simpler way. We can probably say X+5 = 9 find x. 5 is added to a number to get 9 we just assign a variable to X and X+5 = 9 is called an equation and it helps us write the large problem in a simpler way. Equation X+5 = 9 has just one variable which is X and it's unknown also highest power of X is one, this kind of equations are called Linear equations in One Variable, they also referred as First Degree Equations in One Variable. According to NCERT Grade 8 Maths Chapter 2 Linear Equations in One Variable an equation categorized into three parts, let's understand with the following equation-
First, we have an equality sign in thecenter,
Second, on the left of the equality sign, the expression is the Left-Hand Side (LHS), and
Third, on the right of the equality sign, the expression is the Right-Hand Side(LHS).
Example- The perimeter of a rectangle is 13cm and its width is cm. Find its length.
Solution: Assume the length of the rectangle to be x cm.
The perimeter of the rectangle = 2 × (length + width)
The perimeter is given to be 13 cm. Therefore,
Length of the rectangle is 15/4 cm
The utility of linear equations is in their diverse applications; different problems on ages, numbers, combination of currency notes, perimeters, and so on can be solved by using linear equations. In this chapter, there are 6 exercises with 65 questions. Below mentioned are the topics of NCERT for Class 8 Maths Chapter 2 Linear Equations in One Variable-
2.2 Solving Equations which have Linear Expressions on one Side and Numbers on the other Side
2.3 Some Applications
2.4 Solving Equations having the Variable on Both Sides
2.5 Some More Applications
2.6 Reducing Equations to Simpler Form
2.7 Equations Reducible to the Linear Form