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7 Linear Equations in One Variable

A famous Persian mathematician Muhammad ibn Musa al-Khwarizmi wrote a
book titled Al-jabr wa’l muqabalah. The word algebra we use today is derived
from al-jabr. The title of the book referred to methods of solving equations.
Al-jabr i.e., restoration meant moving terms to the other side of the equality
sign and muqabalah i.e., reduction meant combining like terms.
In this chapter, we will discuss the methods of solving linear equations in
one variable and study real-life problems involving them.

Equation
An equation is a statement of equality having one or more literals or variables. In fact, an equation
is a condition on a variable. The condition is that the two expressions of which at least one contains
2
2
a variable are equal. For example, 2x + 3 = 7, 3x + 4y = 10, x = 1, 3x + y = 4, etc. are equations.
Linear Equation
An equation having linear polynomials only is called a linear equation. For example, 3x + 4 = 13,
2x + 4 = 5x + y are linear equations. The first one is a linear equation in one variable as it contains
only x.

Solution of a Linear Equation
The value of the variable which satisfies the equation, i.e., makes the statement true is called the
solution or the root of the linear equation.
Example 1: State whether the following equations are satisfied by the respective values of the
variable mentioned.

S. No. Equation Value S. No. Equation Value

(i) x + 2 = 0 x = 2 (iv) 2y + 3 = 9 y = –3

(ii) x – 1 = 7 x = 4 (v) y = 3 y = 6
2
(iii) 3x = 12 x = 4 (vi) 3m – 2 = 16 m = 6

Solution:
Whether the equation
S. No. Equation Value
is satisfied (Yes/No)
(i) x + 2 = 0 x = 2 No
(ii) x – 1 = 7 x = 4 No
contd...