Solve each of the following equations: `(i) (2x-1)/3-(6x-2)/5=1/3` `(ii) 13(y-4)-3(y-9)-5(y+4)=0` `(iii) 2/3(x-5)-1/4(x-2)=9/2`

Explanation

`(i) (2x-1)/3-(6x-2)/5=1/3`
Taking LCM,
`\frac{5(2x-1)-3(6x-2)}{15}=\frac{1}{3}`
`\frac{10x-5-18x+6}{15}=\frac{1}{3}`
`\frac{1-8x}{15}=\frac{1}{3}`
Cross multiply,
`3(1-8x)=15`
`3-24x=15`
`24x=-12`
`x=-\frac{12}{24}`
`x=-\frac{1}{2}`
Therefore, The value of `x` is `x=-\frac{1}{2}`
`(ii) 13(y-4)-3(y-9)-5(y+4)=0`
`=> 13y - 52 - 3y + 27 - 5y - 20 = 0`
`=> 13y - 3y - 5y - 52 + 27 - 20 = 0`
`=> (13-3-5)y - 72 + 27 = 0`
`=> (13-8)y - 45 = 0`
`=> 5y - 45 = 0`
`=> 5y = 45`
Divide each term by `5` , we get
`=> y = 9`
Therefore,value of `y = 9`
`(iii) 2/3(x-5)-1/4(x-2)=9/2`
`=> { ( 2x - 10 )/ 3 } - { (x + 2)/ 4 } = 9/2`
`=> { (4(2x - 10))/ 12 } - { (3(x + 2))/ 12 } = 9/2`
`=> { ( 8x - 40 )/ 12 } - { (3x + 6)/ 12 } = 9/2`
`=> { ( 8x - 40 ) - (3x + 6) }/ 12 = 9/2`
`=> ( 5x - 46 )/ 12 = 9/2`
`=> ( 5x - 46 ) = (9 xx 12) / 2`
`=> ( 5x - 46 ) = 54/2`
`=> ( 5x - 46 ) = 27`
`=> 5x = 27 + 46`
`=> 5x = 73`
`=> x = 73/5`