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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`
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Solution
`"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`
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