Answer:
The simplest form of (5/6)y + 1 = (1/2)y + (1/2) is -(5/6).
Explanation:
(Given equation is (5/6)y + 1 = (1/2)y + (1/2)
⇛ (5/6)y - (1/2)y = (1/2) - 1
⇛{(5/6) - (1/2)}y = (1/2) - (1/1)
Take the LCM of the denominator 2 and 6 is 6 in LHS.
⇛{(5*1 - 1*3)/6}y = (1/2) - (1/1)
Again take the LCM of the denominator 1 and 2 is 2.
⇛{(5 - 3)/6}y = {1*1 - 1*2)/2}
⇛(2/6)y = {(1- 2)/2}
⇛(2/6)y = -(1/2)
Shift the number (2/6) from LHS to RHS, changing it's sign.
⇛y = -(1/2) - (2/6)
Take the LCM of the denominator 2 and 6 is 6 in RHS.
⇛y = {(-1*3 - 2*1)/6}
⇛y = {(-3 - 2)/6}
⇛y = -(5/6)
Therefore, y = -(5/6) →[simplest form]
Answer: Hence, the simplest form of the equation: (5/6)y + 1 = (1/2)y + (1/2) for the given problem is -(5/6).
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