Question

Find the value of x :- $\: \frac{1 \: - \: \frac{1 \: + \: \frac{ \: 1 \: - \: x \: }{3} }{3} }{4} = 1$​

Answer 1

Given :-

$\sf \: \dfrac{1 \: - \: \dfrac{1 \: + \: \dfrac{ \: 1 \: - \: x \: }{3} }{3} }{4} = 1$

Need to Find Out :-

• Value of x

Solution :-

$\sf \purple {:\implies \: \dfrac{1 \: - \: \dfrac{ \dfrac{ \: (1 \times 3) + (1 \: - \: x \: )}{3} }{3} }{4} = 1} \\ \\ \sf: \implies \: \dfrac{1 \: - \: \dfrac{ \dfrac{ \:( 3 \: + \: 1 \: - \: x \:) }{3} }{3} }{4} = 1 \\ \\ \sf :\implies \: \dfrac{1 \: - \: \dfrac{ \dfrac{ \: (4 \: - \: x) \: }{3} }{3} }{4} = 1 \\ \\ \sf :\implies \: \dfrac{1 \: - \bigg\{ \: \dfrac{( \: 4 - x \: )}{3} \: \times \dfrac{1}{3} \bigg \} }{4} \: = \: 1 \\ \\ \sf: \implies \: \dfrac{1 \: \: - \: \: \dfrac{( \: 4 - x \: )}{9} \: }{4} \: = \: 1 \\ \\ \sf: \implies \: \dfrac{ \dfrac{ (1 \times 9) \: - (1 \times (\: 4 - x) \: )}{9} \: }{4} \: = \: 1 \\ \\ \\ \sf: \implies \: \dfrac{ \dfrac{( 9 \: - \: 4 \: + \: x\: )}{9} \: }{4} \: = \: 1 \\ \\ \sf :\implies \: \dfrac{ \dfrac{5 + x}{9} }{4} = 1 \\ \\ \\ \sf :\implies \: \dfrac{(5 + x)}{9} \times \dfrac{1}{4} \: = \: 1 \\ \\ \\ \sf :\implies \: 5 + x = 36 \times 1 \\ \\ \sf :\implies \: 5 + x = 36 \\ \\ \sf :\implies \: x \: = 36 \: - 5 \\ \\ \sf :\implies\underline\purple{{ \: x \: = \: \bold{31}}}$

Answer 2

$\\ \\ \sf: \implies \: \frac{ \frac{( 9 \: - \: 4 \: + \: x\: )}{9} \: }{4} \: = \: 1 \\ \\ \sf :\implies \: \frac{ \frac{5 + x}{9} }{4} = 1 \\ \\ \\ \sf :\implies \: \frac{(5 + x)}{9} \times \frac{1}{4} \: = \: 1 \\ \\ \\ \sf :\implies \: 5 + x = 36 \times 1 \\ \\ \sf :\implies \: 5 + x = 36 \\ \\ \sf :\implies \: x \: = 36 \: - 5 \\ \\ \sf :\implies\underline{ \: x \: = \: \bold{31}}$