Solve the following equations : x-9 x-5 =5 7 - Vidyadip

Question

Solve the following equations :

$\frac{x-9}{x-5}=\frac{5}{7}$

✓

Answer

$\frac{x-9}{x-5}=\frac{5}{7}$
$\therefore \frac{x-9}{x-5} \times 7(x-5)=\frac{5}{7} \times 7(x-5)$
...[Multiplying both the sides by $7(x-5)$ ]
$\therefore 7(x-9)=5(x-5)$
$\therefore 7 x-63=5 x-25$
$\therefore 7 x-63+63=5 x-25+63$
... [Adding 63 on both the sides]
$\therefore 7 x=5 x+38$
$\therefore 7 x-5 x=5 x+38-5 x$
...[Subtracting $5 x$ from both the sides]
$\therefore 2 x=38$
$\therefore \frac{2 x}{2}=\frac{38}{2} \ldots$ [Dividing both the sides by 2 ]
$\therefore x=19$

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