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Question
Solve the following equations for the unknown: `(1)/(2)(y - 1/3) + (1)/(4)(2y + 1/5) = (3)/(4)(y - 1/12)`
Solution
`(1)/(2)(y - 1/3) + (1)/(4)(2y + 1/5) = (3)/(4)(y - 1/12)`
⇒ `y/(2) - (1)/(6) + y/(2) + (1)/(20) = (3y)/(4) - (1)/(16)`
⇒ `y/(2) + y/(2) - (3y)/(4) = -(1)/(16) + (1)/(6) - (1)/(20)`
⇒ `y - (3y)/(4) = -(1)/(16) + (1)/(6) - (1)/(20)`
⇒ `(4y - 3y)/(4) = -(-15 + 40 - 12)/(240)`
⇒ `y/(4) = (13)/(240)`
⇒ y = `(13)/(240) xx 4`
⇒ y = `(13)/(60)`.
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