Linear Equations in One Variable - 8th math

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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).

linear equation

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) linear equation ncert question 4

Solution:

Given, linear equation ncert question 4

After transposing 3/7 to RHS, we get

linear equation ncert question 4_1

⇒ x = 2 Answer

Question (5) 6x = 12

Solution

Given, 6x = 12

After transposing 6 to RHS, we get

linear equation ncert question 5_1

⇒ x = 2 Answer

Alternate method

Given, 6x = 12

After dividing both sides by 6, we get

linear equation ncert question 5_2

⇒ x = 2 Answer

Question (6) linear equation ncert question 6_1

Solution:

Given, linear equation ncert question 6_2

After transposing 5 to RHS, we get

⇒ t = 10 × 5

⇒ t = 50 Answer

Alternate method

Given,

linear equation ncert question 6_3

After multiplying both sides by 5, we get

linear equation ncert question 6_3

⇒ t = 50 Answer

Question (7) linear equation ncert question 7_1

Solution:

Given, linear equation ncert question 7_2

After transposing 3 to RHS, we get

⇒ 2x = 18 × 3

⇒ 2x = 54

After transposing 2 to RHS, we get

linear equation ncert question 7_3

⇒ x = 27 Answer

Alternate method

Given, linear equation ncert question 7_4

After multiplying both sides by 3, we get

linear equation ncert question 7_5

⇒ 2x = 54

After dividing both sides by 2, we get

linear equation ncert question 7_6

⇒ x = 27 Answer

Question (8) linear equation ncert question 8_1

Solution:

Given, linear equation ncert question 8_2

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

linear equation ncert question 9_1   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

linear equation ncert question 10_1

linear equation ncert question 10_2    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

linear equation ncert question 11_1

linear equation ncert question 11_2  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

linear equation ncert question 11_3

linear equation ncert question 11_3  Answer

Question (12) linear equation ncert question 12_1

Solution:

Given, linear equation ncert question 12_2

After transposing 1 to RHS, we get

linear equation ncert question 12_3

After transposing 3 to RHS, we get

linear equation ncert question 12_4

linear equation ncert question 12_5  Answer

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