## NCERT Solutions for class 8 Maths Chapter 2: Linear Equations in one variable## Exercise 2.1
Subtracting 2x from both the sides, 3x - 2x = 2x + 18 - 2x 3x - 2x = 2x- 2x + 18 x = 0 + 18 x = 18
Transposing 3t to the LHS (Left Hand Side), 5t - 3 - 3t = - 5 5t - 3t - 3 = - 5 2t - 3 = - 5 Transposing (- 3) to the RHS (Right Hand Side), 2t = - 5 + 3 2t = - 2 Dividing by 2, 2t/2 = - 2/2 t = - 1 ## Note: Transposing of a number always results in the change of the sign of that number.
Transposing 3x to the LHS (Left Hand Side), 5x + 9 - 3x = 5 5x - 3x + 9 = 5 2x + 9 = 5 Transposing (9) to the RHS (Right Hand Side), 2x = 5 - 9 2x = -4 Dividing by 2, 2x/2 = -4/2 x = -2
Transposing 2z to the LHS, 4z + 3 - 2z = 6 4z - 2z + 3 = 6 2z + 3 = 6 Subtracting 3 from both the sides, 2z + 3 - 3 = 6 - 3 2z + 0 = 3 2z = 3 Dividing by 2, 2z/2 = 3/2 z = 3/2
Transposing - x to LHS, 2x - 1 + x = 14 2x + x - 1 = 14 3x - 1 = 14 Adding 1 to both the sides, 3x - 1 + 1 = 14 + 1 3x + 0 = 15 3x = 15 Dividing by 3, 3x/3 = 15/3 x = 5
Let's open the brackets. 8x + 4 = 3x - 3 + 7 8x + 4 = 3x + 4 Transposing 3x to the LHS, 8x - 3x + 4 = 4 5x + 4 = 4 Subtracting 4 from both the sides, 5x + 4 - 4 = 4 - 4 5x + 0 = 0 5x = 0 x = 0
Let's open the brackets first on right side. x = 4x/5 + 4/5 × 10 x = 4x/5 + 8 Multiplying the equation by 5, 5x = 5 × (4x/5 + 8) 5x = 4x + 40 Transposing 4x to LHS, 5x - 4x = 40 x = 40
Multiplying the equation by 15, 15 × (2x/3 + 1) = 15 × (7x/15 + 3) 10x + 15 = 7x + 45 Subtracting 15 from both the sides, 10x + 15 - 15 = 7x + 45 - 15 10x + 0 = 7x + 30 10x = 7x + 30 Transposing 7x to LHS, 10x - 7x = 30 3x = 30 Dividing by 3, 3x/3 = 30/3 x = 10
Multiplying the equation by 3, 3 × (2y + 5/3) = 3 × (26/3 - y) 6y + 5 = 26 - 3y Transposing (- 3y) to LHS, 6y + 3y + 5 = 26 9y + 5 = 26 Subtracting 5 from both the sides, 9y + 5 - 5 = 26 - 5 9y = 21 Dividing by 9, 9y/9 = 21/9 y = 21/9 y = 7/3
Transposing 5m to LHS, 3m - 5m = - 8/5 - 2m = - 8/5 Negative sign on the both sides will be cancelled. 2m = 8/5 Multiplying the equation by 5, 2m × 5 = 8/5 × 5 10m = 8 Dividing by 10, 10m/10 = 8/10 m = 8/10 m = 4/5 We can check LHS and RHS by substituting the value of the variable in the equation. ## Exercise 2.2
60 × (x/2 - 1/5) = 60 × (x/3 + 1/4) 30x - 12 = 20x + 15 Transposing 20x to LHS, 30x - 20x - 12 = 15 10x - 12 = 15 Adding 12 to both the sides, 10x - 12 + 12 = 15 + 12 10x + 0 = 27 10x = 27 Dividing by 10, 10x/10 = 27/10 x = 27/10
12 × (n/2 - 3n/4 + 5n/6) = 12 × 21 6n - 9n + 10n = 252 7n = 252 Dividing by 7, 7n/7 = 252/7 n = 36
6 × (x + 7 - 8x/3) = 6 × (17/6 - 5x/2) 6x + 42 - 16x = 17 - 15x 42 - 10x = 17 - 15x Transposing (- 15x) to LHS, 42 - 10x + 15x = 17 42 + 5x = 17 Subtracting 42 from both the sides, 42 + 5x - 42 = 17 - 42 5x + 0 = - 25 5x = - 25 Dividing by 5, 5x/5 = - 25/5
15 × ((x - 5)/3) = 15 × ((x - 3)/5) 5(x - 5) = 3 (x - 3) Opening the brackets, 5x - 25 = 3x - 9 Transposing 3x to LHS, 5x - 3x - 25 = - 9 2x - 25 = - 9 Adding 25 to both the sides, 2x - 25 + 25 = - 9 + 25 2x = 16 Dividing by 2, 2x/2 = 16/2
12 × ((3t - 2)/4 - (2t + 3)/3) = 12 × (2/3 - t) 3 (3t - 2) - 4 (2t + 3) = 8 - 12t 9t - 6 - 8t - 12 = 8 - 12t t - 18 = 8 - 12t Transposing (- 12t) to LHS, t - 18 + 12t = 8 13t - 18 = 8 Adding 18 to both the sides, 13t - 18 + 18 = 8 + 18 13t + 0 = 26 13t = 26 Dividing by 13, 13t/13 = 26/13
6 × (m - (m - 1)/2) = 6 × (1 - (m - 2)/3) 6m - 3(m - 1) = 6 - 2(m - 2) 6m - 3m + 3 = 6 - 2m + 4 3m + 3 = 10 - 2m Transposing (- 2m) to PHS, 3m + 3 + 2m = 10 5m + 3 = 10 Subtracting 3 from both the sides, 5m + 3 - 3 = 10 - 3 5m + 0 = 7 5m = 7 Dividing by 5, 5m/5 = 7/5 m = 7/5
Let's open the brackets. 3t - 9 = 10t + 5 Transposing 10t to LHS, 3t - 10t - 9 = 5 - 7t - 9 = 5 Adding 9 to both the sides, - 7t - 9 + 9 = 5 + 9 - 7t + 0 = 14 - 7t = 14 Dividing by - 7, - 7t/-7 = 14/-7 t = - 14/7
The equation after opening the brackets becomes, 15y - 60 - 2y + 18 + 5y + 30 = 0 15y - 2y + 5y - 60 + 18 + 30 = 0 18y - 12 = 0 Adding 12 to both the sides, 18y - 12 + 12 = 0 + 12 18y + 0 = 12 18y = 12 Dividing by 18, y = 12/18
The equation after opening the brackets becomes, 15z - 21 - 18z + 22 = 32z - 52 - 17 - 3z + 1 = 32z - 69 Transposing - 3z to RHS, 1 = 32z + 3z - 69 1 = 35z - 69 Adding 69 to both the sides, 1 + 69 = 35z - 69 + 69 70 = 35z + 0 70 = 35z Dividing by 35, z = 70/35 z = 2
The equation after opening the brackets becomes, f - 0.75 = 0.5f - 0.45 Transposing 0.5z to LHS, f - 0.5 f - 0.75 = - 0.45 0.5f - 0.75 = - 0.45 Adding 0.75 to both the sides, 0.5f - 0.75 + 0.75 = - 0.45 + 0.75 0.5f + 0 = 0.30 0.5f = 0.30 Dividing by 0.5, 0.5f/0.5 = 0.30/0.5 f = 0.6 |