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`