Question

(x+3) : (x+11) = (x-2) : (x+11) solve this equation​

Answer 1

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$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\large \green{ \bold{ \underline{ \underline{step \: by \: step \: explaination}}}}$

$\: \: \quad \implies \displaystyle \sf{ \frac{(x + 3)}{(x + 11)} = \frac{(x - 2)}{(x + 11)} }$

$\: \: \\ \quad \implies \displaystyle \sf{(x + 3)(x + 11) = (x + 11)(x - 2)}$

$\: \: \\ \quad \implies \displaystyle \sf{x(x + 11) + 3(x + 11) = x(x + 11) - 2(x + 11)}$

$\: \\ \quad \implies \displaystyle \sf{ {x}^{2} + 11x + + 3x + 33 = {x}^{2} + 11x - 2x - 22}$

$\: \: \\ \quad \implies \displaystyle \sf{ {x}^{2} + 14x + 33 = {x}^{2} + 9x - 22}$

$\: \\ \quad \implies \displaystyle \sf{ {x}^{2} + 14x + 33 - {x}^{2} - 9x + 22 = 0}$

$\: \quad \implies \displaystyle \sf{14x - 9x + 33 + 22 = 0}$

$\: \: \quad \implies \displaystyle \sf{5x + 55 = 0}$

$\: \: \quad \implies \displaystyle \sf{x = \frac{ - 55}{5} }$

$\: \: \quad \implies \displaystyle \sf{x = \color{red} \cancel \frac{ - 55}{5} } = \color{green} -11$

$\: \: \implies \displaystyle \sf{x = \color{red} - 11}$

$\: \pink \heartsuit \boxed{ \boxed{ \bold{ \underline{ \underline{ \: the \: answer \: will \: be \: x = - 11}}}}}$