Linear Equations in One Variable - 8th math
Introduction
An algebraic expression in the form of equation involving only linear polynomials is called the Linear Equation. In an algebraic equation there is a sign of equality between two algebraic expressions.
Example:
(1) 2x – 3 = 7
(2) y + 2 = 10
(3) 3y + 6 = 18
(4) 5x + 8x = 182
(5) 2x + 3y = 5
(6) x2 – 3x – 10 = 0
Linear Equation in One Variable
A linear equation with linear expressions in one one variable only is called as Linear Equation in One Variable.
Example:
(1) 8x + 3 = 27
(2) 5x – 7 = 4
(3) 5x + 8x = 182
RHS and LHS
The right side of an algebraic equation is called RHS (Right Hand Side).
The left side of an algebraic equation is called LHS (Left Hand Side).
In an equation the values of the expressions on the LHS and RHS are equal. This happens to be true only for certain values of the variables. These values are the solutions of the equation.
NCERT Exercise 2.1
Solve the following equations.
Question (1) x – 2 = 7
Solution:
Given, x – 2 = 7
By transposing 2 to the right hand side (RHS), we get
⇒ x= 7 + 2
⇒ x = 9 Answer
Alternate method
Given, x – 2 = 7
By adding 2 to the both sides, i.e. to RHS and LHS, we get
⇒ x – 2 + 2 = 7 + 2
⇒ x = 9 Answer
Question (2) y + 3 = 10
Solution:
Given, y + 3 = 10
After subtracting 3 from both sides, i.e. from RHS and LHS, we get
⇒ y + 3 – 3 = 10 – 3
⇒ y = 7 Answer
Alternate method
Give, y + 3 = 10
After transposing 3 to RHS, we get
⇒ y = 10 – 3
⇒ y = 7 Answer
Question (3) 6 = z + 2
Solution:
Given, 6 = z + 2
After transposing 2 to LHS, we get
⇒ 6 – 2 = z
⇒ 4 = z
After rearranging, we get
⇒ z = 4 Answer
Alternate method
Given, 6 = z + 2
After subtracting 2 from both sides, we get
⇒ 6 – 2 = z + 2 – 2
⇒ 4 = z
After rearranging, we get
⇒ z = 4 Answer
Question (4) 
Solution:
Given, 
After transposing 3/7 to RHS, we get
⇒ x = 2 Answer
Question (5) 6x = 12
Solution
Given, 6x = 12
After transposing 6 to RHS, we get
⇒ x = 2 Answer
Alternate method
Given, 6x = 12
After dividing both sides by 6, we get
⇒ x = 2 Answer
Question (6) 
Solution:
Given, 
After transposing 5 to RHS, we get
⇒ t = 10 × 5
⇒ t = 50 Answer
Alternate method
Given,
After multiplying both sides by 5, we get
⇒ t = 50 Answer
Question (7) 
Solution:
Given, 
After transposing 3 to RHS, we get
⇒ 2x = 18 × 3
⇒ 2x = 54
After transposing 2 to RHS, we get
⇒ x = 27 Answer
Alternate method
Given,
After multiplying both sides by 3, we get
⇒ 2x = 54
After dividing both sides by 2, we get
⇒ x = 27 Answer
Question (8) 
Solution:
Given, 
After transposing 1.5 to LHS, we get
⇒ 1.6 × 1.5 = y
⇒ 2.40 = y
⇒ y = 2.4 Answer
Question (9) 7x – 9 = 16
Solution:
Given, 7x – 9 = 16
After transposing 9 to RHS, we get
⇒ 7x = 16 + 9
⇒ 7x = 25
After transposing 7 to RHS, we get
Answer
Question (10) 14 y – 8 = 13
Solution :
Given, 14 y – 8 = 13
After transposing 8 to RHS, we get
⇒ 14 y = 13 + 8
⇒ 14 y = 21
After transposing 14 to RHS, we get
Answer
Question (11) 17 + 6 p = 9
Solution:
Given, 17 + 6 p = 9
After transposing 17 to RHS, we get
⇒ 6 p = 9 – 17
⇒ 6 p = – 8
After transposing 6 to RHS, we get
Answer
Alternate method
Given, 17 + 6 p = 9
After subtracting 17 from both sides, we get
⇒ 17 + 6 p – 17 = 9 – 17
⇒ 6p = – 8
After diving both sides by 6, we get
Answer
Question (12) 
Solution:
Given, 
After transposing 1 to RHS, we get
After transposing 3 to RHS, we get
Answer
Reference: