8th Maths 2.5

Chapter 2

Linear Equations in One Variable

NCERT Class 8th solution of Exercise 2.1

NCERT Class 8th solution of Exercise 2.2

NCERT Class 8th solution of Exercise 2.3

NCERT Class 8th solution of Exercise 2.4

NCERT Class 8th solution of Exercise 2.6

Exercise 2.5

Solve the following linear equations.

Q1. `text{x}/2 - 1/5 = text{x}/3 + 1/4`

`text{Sol.}`

`text{x}/2 - 1/5 = text{x}/3 + 1/4`

`text{x}/2 - text{x}/3 = 1/4 + 1/5`

`text{3x - 2x}/6 = (5 + 4)/20`

`text{x}/6 = 9/20`

`text{x} = (6 times 9)/20`

`text{x} = (3 times 9)/10`

`text{x} = 27/10`

`text{Answer:}`

`text{x} = 27/10`.

Q2. `text{n}/2 - text{3n}/4 + text{5n}/6 = 21`

`text{Sol.}`

`text{n}/2 - text{3n}/4 + text{5n}/6 = 21`

`text{6n - 9n + 10n}/12 = 21`

`text{7n}/12 = 21`

`text{n} = (21 times 12)/7`

`text{n} = 36`

`text{Answer:}`

`text{n} = 36.`

Q3. `text{x + 7 -} text{8x}/3 = 17/6 - text{5x}/2`

`text{Sol.}`

`text{x} + 7 - text{8x}/3 = 17/6 - text{5x}/2`

`text{x} - text{8x}/3 + text{5x}/2 = 17/6 - 7`

`text{6x - 16x + 15x}/6 = (17 - 42)/6`

`text{5x}/6 = - 25/6`

`text{5x} = - 25`

`text{x} = - 5`

`text{Answer:}`

`text{x} =  - 5`

Q4. `text{x - 5}/3 = text{x - 3}/5`

`text{Sol.}`

`text{x - 5}/3 = text{x - 3}/5`

`5text{x - 5} = 3text{x - 3}`

`text{5x - 25 = 3x - 9}`

`text{5x - 3x } = 25 - 9`

`text{2x} = 16`

`text{x} = 16/2`

`text{x} = 8`

`text{Answer:}`

`text{x} = 8.`

Q5. `text{3t - 2}/4 - text{2t + 3}/3 = 2/3 -text{t}`

`text{Sol.}`

`text{3t - 2}/4 - text{2t + 3}/3 = 2/3 - text{t}`

`text{3t - 2}/4 - text{2t + 3}/3 + text{t} = 2/3`

`text{9t - 6 - 8t - 12 + 12t}/12 = 2/3`

`text{13t - 18}/12 = 2/3`

`text{13t - 18} = (2 times12)/3`

`text{13t - 18} = 8`

`text{13t} = 8 + 18`

`text{t} = 26/13`

`text{t} = 2`

`text{Answer:}`

`text{t} = 2`.

Q6. `text{m } - text{m - 1}/2 = 1 - text{m - 2}/3`

`text{Sol.}`

`text{m } - text{m - 1}/2 = 1 - text{m - 2}/3`

`text{m } - text{m - 1}/2 + text{m - 2}/3 = 1`

`text{6m - 3m + 3 + 2m - 4}/6 = 1`

`text{5m - 1}/6 = 1`

`text{5m} = 6 + 1`

`text{5m} = 7`

`text{m} = 7/5`

`text{Answer:}`

`text{m } =7/5`.

Simplify and solve the following linear equations.

Q7. `text{3(t - 3) = 5(2t + 1)}`

`text{Sol.}`

`text{3(t - 3) = 5(2t + 1)}`

`text{3t} - 9 = text{10t} + 5`

`text{3t - 10t} = 5 + 9`

`text{- 7t} = 14`

`text{t} = - 14/7`

`text{t} = - 2`

`text{Answer:}`

`text{t} = - 2`.

Q8. `text{15(y - 4) - 2(y - 9) + 5(y + 6) = 0}`

`text{Sol.}`

`text{15(y - 4) - 2(y - 9) + 5(y + 6) = 0}`

`text{15y} - 60 - text{ 2y} + 18 + text{ 5y} + 30 = 0`

`text{15y - 2y + 5y - 60 + 18 + 30 = 0`

`text{18y} - 12 = 0`

`text{18y} = 12`

`text{y} = 12/18`

`text{y} = 2/3`  

`text{Answer:}`

`text{y} = 2/3`.

Q9. `text{3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17}`

`text{Sol.}`

`text{3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17}`

`text{15z - 21 - 18z + 22 = 32z - 52 -17}`

`text{15z - 18z - 32z = 21 - 22 - 52 - 17`

`text{- 35z} = - 70`

`text{z} = 70/35`

`text{z} = 2` 

`text{Answer:}`

`text{z} = 2`.

Q10. `0.25(4f - 3) = 0.05(10f - 9)`

`text{Sol.}`

`0.25(4f - 3) = 0.05(10f - 9)`

`1.00f - 0.75 = 0.5f - 0.45`

`1f - 0.5f = 0.75 - 0.45`

`0.5f = 0.30`

`f = 0.30/0.5`

`f = 0.6`

`text{Answer:}`

`f = 0.6.`