Question

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

Answer 1

$\large{\underline{\underline{\mathfrak{\red{\sf{Answer-}}}}}}$

$\boxed{x=5}$

$\large{\underline{\underline{\mathfrak{\red{\sf{Explanation-}}}}}}$

Given expression :

• $\sf{(x+3):(x+11)=(x-2):(x+1)}$

To find :

• Value of x.

Solution :

$\sf{(x+3):(x+11)=(x-2):(x+1)}$

$\implies$ $\sf{\dfrac{x+3}{x+11}+\dfrac{x-2}{x+1}}$

By cross multiplying,

$\implies$ $\sf{(x+1)(x+3)=(x-2)(x+11)}$

Solving it by horizontally method,

$\implies$ x(x+3)+1(x+3) = x(x+11)-2(x+11)

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

$\implies$ 4x - 9x = -22 - 3

$\implies$ -5x = -25

$\implies$ x = $\sf{\cancel{\dfrac{-25}{-5}}}$

$\implies$ $\boxed{x=5}$

Answer 2

Question :

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

Solution :

$\underline{\bold{Given:}}$

• (x+3) : (x+11) = (x-2) : (x+1)

$\underline{\bold{To\:Find:}}$

• The value of x.

$\implies (x+3) : (x+11) = (x-2) : (x+1) \\ \implies\frac{x + 3}{x + 11} = \frac{x - 2}{x + 1} \\\implies ( x + 1)(x + 3) = (x - 2)(x + 11) \\\implies x(x + 3) + 1(x + 3) = x(x + 11) - 2(x + 11) \\ \implies x^2 + 3x + x + 3= x^2 + 11x - 2x - 22 \\ \implies x^2 + 4x + 3 = x^2 + 9x - 22 \\ \implies x^2 + 4x - x^2 - 9x = - 22 - 3\\ \implies - 5x = - 25\\ \implies x = \frac{ - 25}{ - 5} \\ \implies x = 5$

$\boxed {\green{\therefore{The\:value\:of\:x\:is\:5.}}}$