Question

Solve: `"2x"/3 - ("x" - 1)/6 + ("7x" - 1)/4 = 2 1/6` Hence, find the value of 'a', if `1/"a" + 5"x" = 8`

Answer 1

`"2x"/3 - ("x" - 1)/6 + ("7x" - 1)/4 = 2 1/6`

`=> "2x"/3 - ("x" - 1)/6 + ("7x" - 1)/4 = 13/6`

`("8x" - "2x" + 2 + "21x" - 3 = 26)/12`  ...(L.C.M. of 3, 6, 4, 6 = 12)

⇒ 27x - 1 = 26

⇒ 27x = 26 + 1

⇒ x = `27/27` = 1

Now, `1/"a" + 5"x" = 8`

`=> 1/"a" + 5 xx 1 = 8`

`=> 1/"a" + 5 = 8`

`=> 1/"a" = 8 - 5 = 3`

∵ 3a = 1

`=> "a" = 1/3`

∴ x = 1 and a = `1/3`