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Solve the following equations:

i. 3 (y + 8) = 10 (y – 4) + 8

ii. \(\cfrac{x-9}{x-5} =\cfrac{5}{7}\)

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i. 3 (y + 8) = 10 (y – 4) + 8 

∴ 3y + 24 = 10y – 40 + 8 

∴ 3y + 24 = 10y – 32 

∴ 3y + 24 – 24 = 10y – 32 – 24 

…[Subtracting 24 from both the sides] 

∴ 3y = 10y – 56 

∴ 3y – 10y = 10y – 56 

…[Subtracting 10y from both the sides] 

∴ – 7y = – 56

∴ \( \cfrac{-7y}{-7}=\cfrac{-56}{-7}\)…[Dividing both the sides by – 7]

∴ y = 8

 ii. \(\cfrac{x-9}{x-5} =\cfrac{5}{7}\)

…[Multiplying both the sides by 7 (x – 5)] 

∴7 (x – 9) = 5 (x – 5) 

∴7x – 63 = 5x – 25 

∴7x – 63 + 63 = 5x – 25 + 63 

…[Adding 63 on both the sides] 

∴7x = 5x + 38 

∴7x – 5x = 5x + 38 – 5x 

…[Subtracting 5x from both the sides] 

∴ 2x = 38

\(\cfrac{2x}{2} =\cfrac{38}{2}\)…[Dividing both the sides by 2]

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