Question

.
Solve.
(x – 6)(x + 7) = (x + 3)(x – 11)
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Answer 1

Answer:

$x ^{2} + 7x - 6x - 42 = x^{2} - 11x + 3x - 33$

$x {}^{2} + x - 42 = x {}^{2} - 8x - 33$

$x + 8x = - 33 + 42$

$9x = 9$

$x = 1$

Answer 2

(x - 6)(x + 7) = (x + 3)(x - 11)

⇒ x(x + 7) -6(x + 7) = x(x - 11) + 3(x - 11)

⇒ x² + 7x - 6x - 42 = x² - 11x + 3x - 33

⇒ x² + x - 42 = x² - 8x - 33

Cancelling x² on both sides,

x - 42 = - 8x - 33

⇒ 9x = 9

∴ x = 1