Question

Solve:
$\frac{y - 8}{3} = \frac{7 - 4y}{7}$
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Answer 1

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$\huge\star\:\:{\orange{\underline{\pink{\mathbf{Answer}}}}}$

$we \: have \: \frac{y - 8}{3} = \frac{7 - 4y}{7}$

The denominator of Lhs and RHS are 3 and 7 respectively. multiplying both sides by the LCM of 3 and 7, that is 21, we get

$</em><em>⟹</em><em>21( \frac{y - 8}{3}) = 21( \frac{7 - 4y}{7} )$

$</em><em>⟹</em><em> 7(y - 8) = 3(7 - 4y) \\ </em><em>$

$</em><em>⟹</em><em>7y - 56 = 21 - 12y$

$</em><em>⟹</em><em>1</em><em>9y = 77$

$</em><em>⟹</em><em>y = \frac{77}{19}$

$</em><em>T</em><em>hus \: y = \frac{77}{19} \: is \: the \: solution \: of \: the \: given \: equation.$

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$\huge\underline\bold\orange{Check}$

$putting \: y = \frac{77}{19} \: in \: the \: given \: equation \: we \: get$

$\large \bold{\underline{\sf{\blue{L.H S.}}}}$

$L.H.S = \frac{y - 8}{3} = \frac{ \frac{77}{19 } -8 }{3} = \frac{77 - 152}{19 \times 3} = \frac{ - 75}{57} = \frac{ - 25}{19}$

$\large \bold{\underline{\sf{\blue{R.H.S.}}}}$

$R.H.S = \frac{7 - 4y}{7}$

$= \frac{7 - 4 \times \frac{77}{19} }{7} = \frac{7 - \frac{308}{19} }{7} = \frac{133 - 308}{7 \times 19} = \frac{ - 175}{7 \times 19} = \frac{ - 25}{19} \\ Thus \: L.H.S. = R.H.S. \: for \: y = \frac{77}{19}$

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${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$

${\huge{\underline{\small{\mathbb{\pink{</p><p>~AngelicCandy♡ :)}}}}}}$

Answer 2

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$\huge\star\:\:{\orange{\underline{\pink{\mathbf{Answer}}}}}$

$we \: have \: \frac{y - 8}{3} = \frac{7 - 4y}{7}$

The denominator of Lhs and RHS are 3 and 7 respectively. multiplying both sides by the LCM of 3 and 7, that is 21, we get

⟹ $21( \frac{y - 8}{3}) = 21( \frac{7 - 4y}{7}$

$\begin{gathered}⟹ 7(y - 8) = 3(7 - 4y) \\\end{gathered}$

⟹7y - 56 = 21 - 12y⟹7y−56=21−12y

⟹19y = 77⟹19y=77

⟹ $y = \frac{77}{19}$

$\begin{gathered}Thus \: y = \frac{77}{19} \: is \: the \: solution \: of \: the \: given \: equation. \\\end{gathered}$

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