# Linear Equations

## Exercise 2.5 Part 1

##### Solution of NCERT Exercise from Question 1 to 5

Solve the following linear equations:

Question 1: x/2-1/5=x/3+1/4

Solution: Given x/2-1/5=x/3+1/4

After transposing x/3 to LHS and -1/5 to RHS we get:

x/2-x/3=1/4+1/5

Or, (3x-2x)/(6)=(5+4)/(20)

Or, x/6=(9)/(20)

After multiplying both sides with 6, we get:

x/6xx6=(9)/(20)xx6=(54)/(20)

Or, x=(27)/(10)

Question 2: n/2-(3n)/(4)+(5n)/(6)=21

Solution: Given n/2-(3n)/(4)+(5n)/(6)=21

Or, (6n-9n+10n)/(12)=21

Or, (-3n+10n)/(12)=21

Or, (7n)/(12)=21

After multiplying both sides by 12, we get:

(7n)/(12)xx12=21xx12

Or, 7n=252

Now, after dividing both sides by 7, we get:

(7n)/(7)=(252)/(7)

Or, n=36

Question 3: x+7-(8x)/(3)=(17)/(6)-(5x)/(2)

Solution: Given x+7-(8x)/(3)=(17)/(6)-(5x)/(2)

Or, x-(8x)/(3)+7=(17)/(6)-(5x)/(2)

After transposing 7 to RHS and -(5x)/(2) to LHS we get:

x-(8x)/(3)+(5x)/(2)=(17)/(6)-7

Or, (6x-16x+15x)/(6)=(17-42)/(6)

Or, (5x)/(6)=-(25)/(6)

After multiplying both sides with 6, we get:

(5x)/(6)xx6=-(25)/(6)xx6

Or, 5x=-25

After dividing both sides by 5, we get:

(5x)/(5)=-(25)/(5)

Or, x=-5

Question 4: (x-5)/(3)=(x-3)/(5)

Solution: Given, (x-5)/(3)=(x-3)/(5)

After multiplying both sides with 3, we get:

(x-5)/(3)xx3=(x-3)/(5)xx3

Or, (x-5)=((x-3)3)/(5)

After multiplying both sides with 5, we get:

(x-5)xx5=((x-3)3)/(5)xx5

Or, (x-5)5=(x-3)3

After removing the brackets from both sides we get:

5x-25=3x-9

After transposing 3x to LHS and -25 to RHS we get:

5x-3x=-9+25

Or, 2x=16

After dividing both sides by 2, we get:

(2x)/(2)=(16)/(2)

Or, x=8

Question 5: (3t-2)/(4)-(2t+3)/(3)=2/3-t

Solution: Given (3t-2)/(4)-(2t+3)/(3)=2/3-t

After transposing -t to LHS, we get:

(3t-2)/(4)-(2t+3)/(3)+t=2/3

Or, (3(3t-2)-4(2t+3)+12t)/(12)=2/3

After removing the brackets, we get:

(9t-6-8t-12+12t)/(12)=2/3

Or, (9t-8t+12t-6-12)/(12)=2/3

Or, (13t-18)/(12)=2/3

After multiplying both sides by 12, we get:

(13t-18)/(12)xx12=2/3xx12

Or, 13t-18=(24)/(3)

After transposing -18 to RHS, we get:

13t=(24)/(3)+18

Or, 13t=(24+54)/(3)=(78)/(3)=26

Or, 13t=26

By dividing both sides by 13, we get:

(13t)/(13)=(26)/(13)

Or, t=2