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Question
Solve the following equations for the unknown: `(7 x - 1)/(4) - (1)/(3)(2x - (1 - x)/2) = 5(1)/(3)`
Solution
`(7 x - 1)/(4) - (1)/(3)(2x - (1 - x)/2) = 5(1)/(3)`
⇒ `(7x - 1)/(4) - (2x)/(3) + (1 - x)/(6) = (16)/(3)`
LCM of all the denominators is 12.
Multiply the equation throughout by the LCM.
⇒ `(3(7x - 1))/(12) - (4(2x))/(12) + (2(1 - x))/(12)` = 16(4)
⇒ `(21x - 3)/(12) - (8x)/(12) + (2 - 2x)/(12)` = 64
⇒ 21x - 3 - 8x + 2 - 2x = 64
⇒ 11x = 64 + 3 - 2
⇒ 11x = 65
⇒ x = `(65)/(11)`.
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