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Solve the following equations.

i) 9\(\frac14\) = y - 1\(\frac13\)

ii) x/2 − 4/5 + x/5 + 3x/10 = 1/5

iii) x/2 - 1/4 = x/3 + 1/2

iv) \(\frac{2x\,-\,3}{3x\,+\,3}\) = -2/3

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i) 9\(\frac14\) = y - 1\(\frac13\)

ii) x/2 − 4/5 + x/5 + 3x/10 = 1/5

iii) x/2 - 1/4 = x/3 + 1/2

iv) \(\frac{2x\,-\,3}{3x\,+\,3}\) = -2/3

⇒ 3(2x – 3) = – 2(3x + 2) 

⇒ 6x – 9 = -6x – 4 

⇒ 6x + 6x = -4 + 9 

⇒ 12x = 5 

∴ x = 5/12

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