(x + 3) : (x + 11) = (x – 2) : (x + 1), then find the value of x.

1.	(x + 3) : (x + 11) = (x – 2) : (x + 1), then find the value of x.
Answer» (x + 3) : (x + 11) = (x- 2) : (x+ 1) \(\frac{(x\, +\,3)}{(x\,+\,11)}\) = \(\frac{(x\, -\,2)}{(x\,+\,1)}\) ∴ (x + 3)(x +1) = (x – 2)(x + 11) ∴ x(x +1) + 3(x + 1) = x(x + 11) – 2(x + 11) ∴ x² + x + 3x + 3 = x² + 11x – 2x – 22 ∴ x² + 4x + 3 = x² + 9x – 22 ∴ 4x + 3 = 9x – 22 ∴ 3 + 22 = 9x – 4x ∴ 25 = 5x ∴ x = 5

Answer»

(x + 3) : (x + 11) = (x- 2) : (x+ 1)

\(\frac{(x\, +\,3)}{(x\,+\,11)}\) = \(\frac{(x\, -\,2)}{(x\,+\,1)}\)

∴ (x + 3)(x +1) = (x – 2)(x + 11)

∴ x(x +1) + 3(x + 1) = x(x + 11) – 2(x + 11)

∴ x² + x + 3x + 3 = x² + 11x – 2x – 22

∴ x² + 4x + 3 = x² + 9x – 22

∴ 4x + 3 = 9x – 22

∴ 3 + 22 = 9x – 4x

∴ 25 = 5x

∴ x = 5

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