Question

Find For x:-

$\sf(x - 2) : (x + 2) = (x + 3) : (x + 11)$

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Answer 1

$\sf \red {(x - 2) : (x + 2) = (x + 3) : (x + 11)}$

$\sf :\implies \dfrac{x - 2}{x + 2} = \dfrac{x + 3}{x + 11}$

By cross multiplication:-

$\sf :\implies (x - 2)(x + 11)= (x + 3)(x + 2)$

$\sf :\implies x(x + 11) - 2(x + 11)= x(x + 2) + 3(x + 2)$

$\sf :\implies {x}^{2} + 11x - 2x - 22= {x}^{2} + 2x+ 3x + 6$

$\sf :\implies {x}^{2} + 9x - 22= {x}^{2} + 5x + 6$

$\sf :\implies {x}^{2} - {x}^{2} + 9x - 5x - 22 - 6 = 0$

$\sf :\implies 4x - 28 = 0$

$\sf :\implies 4x = 28$

$\sf :\implies x = \cancel { \dfrac{28}{4}}$

$\sf\underline{ \boxed{ \red{\sf : \implies x = 7}}}$

Verification :-

$\sf (x - 2)(x + 11)= (x + 3)(x + 2)$

$\sf :\implies (7 - 2)(7 + 11)= (7 + 3)(7 + 2)$

$\sf :\implies 5 \times 18 = 10 \times 9$

$\sf \red {: \implies 90 = 90}$

$\sf :\implies$ LHS = RHS

• Hence Verified!!

Answer 2

⠀⠀⠀⠀⠀⠀$\tt\boxed{x = 7}$

Step-by-step explanation:

(x - 2) : (x + 2) = (x + 3) : (x + 11)

(x - 2) / (x + 2) = (x + 3) / (x + 11)

(x - 2) × (x + 11) = (x + 3) × (x + 2)

x(x + 11) - 2(x + 11) = x(x + 2) + 3(x + 2)

x² + 11x - 2x - 22 = x² + 2x + 3x + 6

• x² cancel outs

11x - 2x - 22 = 2x + 3x + 6

9x - 22 = 5x + 6

9x - 5x = 22 + 6

4x = 28

x = 7