NCERT Book Class 8 Maths Chapter 2 Linear Equations in One Variable

LINEAR EQUATIONS IN ONE VARIABLE 15
CHAPTER

Linear Equations in
One Variable 2
2.1 Introduction
In the earlier classes, you have come across several algebraic expressions and equations.
Some examples of expressions we have so far worked with are:
5x, 2x – 3, 3x + y, 2xy + 5, xyz + x + y + z, x2 + 1, y + y2
5 37
Some examples of equations are: 5x = 25, 2x – 3 = 9, 2 y + = , 6 z + 10 = −2
2 2
You would remember that equations use the equality (=) sign; it is missing in expressions.
Of these given expressions, many have more than one variable. For example, 2xy + 5
has two variables. We however, restrict to expressions with only one variable when we
form equations. Moreover, the expressions we use to form equations are linear. This means
that the highest power of the variable appearing in the expression is 1.
These are linear expressions:
5
2x, 2x + 1, 3y – 7, 12 – 5z, ( x – 4) + 10
4
These are not linear expressions:
x2 + 1, y + y2, 1 + z + z2 + z3 (since highest power of variable > 1)
Here we will deal with equations with linear expressions in one variable only. Such
equations are known as linear equations in one variable. The simple equations which
you studied in the earlier classes were all of this type.
Let us briefly revise what we know:
(a) An algebraic equation is an equality
involving variables. It has an equality sign.
The expression on the left of the equality sign
is the Left Hand Side (LHS). The expression 2x – 3 = 7
on the right of the equality sign is the Right
2x – 3 = LHS
Hand Side (RHS).
7 = RHS