Question

2x/3+1 = 3/4(x+1)
solve the equation and check the solution.​

Answer 1

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Question :

$\pink\bigstar\rm{\dfrac{2x}{3+1}=\dfrac{3}{4(x+1)}}$

To find :

The value of x=?

Solution :

$\\ \quad \implies \large \sf \: \frac{2x}{3 + 1} = \frac{3}{4(x + 1)}$

$\\ \quad \implies \large \sf \: \frac{2x}{4} = \frac{3}{4x + 4}$

$\\ \quad \implies \large \sf \: \frac{x}{2} = \frac{3}{4x + 4}$

$\\ \quad\implies \large \sf4 {x}^{2} + 4x = 6$

$\\ \quad \implies \large \sf \: 4 {x}^{2} + 4x - 6 = 0$

$\\ \quad \implies \large \sf \: 2 {x}^{2} + 2x - 3 = 0$

By using formula method :

$\\ \quad \implies \large \sf \: x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

$\\ \quad \implies \large \sf \: x = \frac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 2 \times - 3} }{2 \times 2}$

$\\ \quad \implies \large \sf \: x = \frac{ - 2 \pm \sqrt{4 + 24 } }{4}$

$\\ \quad \implies \large \sf \: x = \frac{ - 2 \pm \sqrt{28} }{4}$

$\\ \quad \implies \large \sf \: x = \frac{ \cancel2( - 1 \pm \sqrt{7}) }{ \cancel2 \times 2}$

$\\ \implies \large \sf \: x = \frac{ - 1 \pm \sqrt{7} }{2}$

$\red \bigstar \large \sf \: roots \: of \: this \: equation \: is \: \: \\ \boxed{ \large \sf \: x = \frac{ - 1 + \sqrt{7} }{2} \: and \: x = \frac{ - 1 - \sqrt{7} }{2} }$