Linear Equations in One Variable - 8th math

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,

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