Solve the following equations and also check your result in each case: `(i) ((3x+1))/(16)+((2x-3))/7=((x+3))/8+((3x-1))/(14)` `(ii) ((1-2x))/7-((2-3x))/8=3/2+x/4` `(iii) (9x+7)/2-\ (x-(x-2)/7)=36` `(iv) 0. 18\ (5x-4)=\ 0. 5 x+0. 8`

Explanation

`(i) ((3x+1))/(16)+((2x-3))/7=((x+3))/8+((3x-1))/(14)`
`=>21 x + 7 + 32 x - 48 / 112 = 7 x + 21 + 12 x - 4 / 56`
`=>53 x - 41 / 112 = 19 x + 17 / 56`
`=> 53 x - 41 = 38 x + 34`
`=> 53 x-38 x = 34 + 41`
`=>15 x = 75`
`=>x = 75/15`
`=> x = 5`

`(ii) ((1-2x))/7-((2-3x))/8=3/2+x/4`
`=>-6+5x/56=6+x/4`
`=>4(-6+5x)=56(6+x)`
`=>-24+20x=336+56x`
`=>20x-56x=336+24`
`=>-36x=360`
`=>x=360/36=10`
`=>x=-10`

`(iii) (9x+7)/2-\ (x-(x-2)/7)=36`
`⇒63x + 49 - 12x- 4 = 504`
`⇒51x + 45 = 504`
`⇒51x = 504- 45`
`⇒51x = 459`
`⇒x = 459/51`
`⇒ x = 9`

`(iv) 0. 18\ (5x-4)=\0. 5 x+0. 8`
`0.18(5x−4)=0.5x+0.8`
`⇒ 0.90x−0.72=0.5x+0.8` ...[By Distribution Law]
Transposing `x` terms to one side, we get,
`⇒ 0.90x−0.5x=0.8+0.72`
`⇒ 0.40x=1.52`
`=>x=19/5`