Question

solve the equation (x+6)/(3x+2)=(x+9)/(3x-1)​

Answer 1

Solution:-

$\rm \to \: \dfrac{(x + 6)}{(3x + 2)} = \dfrac{(x + 9)}{(3x- 1)}$

Now using cross multiplication methods

$\rm \to \: (x + 6)(3x - 1) = (x + 9)(3x + 2)$

Now multiply

$\rm \to \: 3 {x}^{2} - x + 18x - 6 = 3 {x}^{2} + 2x + 27x + 18$

$\rm \to \: \cancel{3 {x}^{2}} - x + 18x - 6 = \cancel{3 {x}^{2} } + 2x + 27x + 18$

$\rm \to \: - x + 18x - 6 = 2x + 27x + 18$

$\rm \to \: - x - 2x + 18x - 27x - 6 - 18 = 0$

$\rm \to \: - 3x - 9x - 24 = 0$

$\rm \to \: - 12x = 24$

$\rm \to \: x = - \dfrac{24}{12}$

$\rm \to \: x = - 2$

Now check the answer

$\rm \to \: \dfrac{(x + 6)}{(3x + 2)} = \dfrac{(x + 9)}{(3x- 1)}$

Put the value of x = -2

$\rm \to \: \dfrac{( - 2+ 6)}{(3 \times - 2 + 2)} = \dfrac{( - 2+ 9)}{(3 \times - 2- 1)}$

$\rm \to \: \dfrac{4}{ - 6 + 2} = \dfrac{7}{ - 6 - 1}$

$\rm \to \: \dfrac{4}{ - 4} = \dfrac{7}{ - 7}$

$\rm \to \: - 1 = - 1$

LHS = RHS

Answer 2

Step-by-step explanation:

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