Question

(x-2) : (x+ 2) = (x +3) : (x + 11) then find value x ​

Answer 1

Step-by-step explanation:

hope that it is useful.

Answer 2

Step-by-step explanation:

Given:-

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

To Find:-

• The value of x

Solution:-

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

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

By cross multiplication:-

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

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

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

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

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

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

$\sf \implies 4x = 28$

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

$\sf \implies x = 7$

$\longrightarrow \underline{\boxed{\rm \therefore \: The \: value \: of \: x = 7 }}$

LET'S Check:-

Substitute x = 7 in $\sf (x - 2)(x + 11)= (x + 3)(x + 2)$

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

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

$\sf \implies 90 = 90$

LHS = RHS

Hence Verified