Question

2-x/ x-5= -3/7 what is the correct answer for this only answer no spammer.
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Answer 1

$\large \bf{\red {Solution...}}$

$: \implies \bf{ \dfrac{2 - x}{x - 5} = \dfrac{ - 3}{7} }$

Cross multiplying them :

$: \implies \bf{7(2 - x) = - 3(x - 5)}$

$: \implies \bf{14 - 7x = - 3x + 15}$

$: \implies \bf{14 - 15 = - 3x + 7x}$

$: \implies \bf{ - 1 = 4x}$

$: \implies \bf{x = \dfrac{ - 1}{4} }$

$\large \bf {\red{Verification....}}$

$: \implies \bf \dfrac{2 - \bigg( \dfrac{ - 1}{4} \bigg) }{ \bigg( \dfrac{ - 1}{4} \bigg) - 5 } = \dfrac{ - 3}{7}$

LCM of 1 and 4 is 4 :

$: \implies \bf \dfrac{ \bigg( \frac{9}{4} \bigg)}{ \bigg( - \frac{ 21}{4} \bigg )}$

Division by reciprocal :

$: \implies \bf \dfrac{9}{4} \times \bigg( - \dfrac{4}{ 21} \bigg)$

4 in the denominator gets cancelled with 4 in the numerator :

$: \implies\bf \dfrac{9}{ \cancel4} \times \bigg( - \dfrac{ \cancel4}{21} \bigg)$

$: \implies\bf - \dfrac{9}{21}$

$: \implies \bf \dfrac{ - 3}{7} = \dfrac{ - 3}{7}$

LHS = RHS

Henceforth, verified!