Question

10.
$\frac{x + 3}{2} = \frac{x - 4}{5}$
11.
$\frac{2x - 1}{3} = \frac{x}{2}$
12.
$\frac{3x + 1}{5} = \frac{2x}{3}$
​

Answer 1

Step-by-step explanation:

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Answer 2

$\bf \underline{ \underline{\maltese\:Solution} }$

$\sf(i) \: \: \: \dfrac{x + 3}{2} \: = \: \dfrac{x - 4}{5}$

$\sf \underline{Doing \: cross \: multiplication},$

$\sf \implies(x + 3) \times 5 = 2(x - 4)$

$\sf \implies5x +15 = 2x - 8$

$\sf \implies 3x + 15 = - 8$

$\sf \implies 3x = - 8 - 15$

$\sf \implies 3x = -23$

$\sf \red{ \implies x = \dfrac{ - 23}{3} }$

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$\sf(ii) \: \: \: \dfrac{2x - 1}{3} \: = \: \dfrac{x}{2}$

$\sf \underline{Doing \: cross \: multiplication},$

$\sf \implies(2x - 1) \times 2 = 3x$

$\sf \implies4x - 2 = 3x$

$\sf \implies4x - 2 - 3x = 0$

$\sf \implies x - 2 = 0$

$\sf \red{ \implies x = 2}$

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$\sf(iii) \: \: \: \dfrac{3x + 1}{5} \: = \: \dfrac{2x}{3}$

$\sf \underline{Doing \: cross \: multiplication},$

$\sf \implies(3x + 1) \times 3 = 5(2x)$

$\sf \implies9x + 3 = 10x$

$\sf \implies9x + 3 - 10x = 0$

$\sf \implies - x + 3 = 0$

$\sf \implies - x = - 3$

$\sf \red{ \implies x = 3}$