Solve equations- using factorization method-3x-22x-3 - 3x-8x-4

Step: Factorising the equation: 3x 22x 3 = 3x 8x+4 ⇒ (3x 2) (x+4) = (3x 8)(2x 3) ⇒ 3x^2 2x +12x 8 = 6x^2 16x 9x +24 ⇒ 3x^2 35x +32 = 0 ⇒ 3x^2 32x nb ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation by Common Factors

Solve equatio...

Question

Solve equations, using factorization method:
$\frac{3 x - 2}{2 x - 3} = \frac{3 x - 8}{x + 4}$

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Solution

Step: Factorising the equation:

$\frac{3 x - 2}{2 x - 3} = \frac{3 x - 8}{x + 4}$

$\Rightarrow$ $(3 x - 2) (x + 4) = (3 x - 8) (2 x - 3)$

$\Rightarrow$ $3 x^{2} - 2 x + 12 x - 8 = 6 x^{2} - 16 x - 9 x + 24$

$\Rightarrow 3 x^{2} - 35 x + 32 = 0$

$\Rightarrow 3 x^{2} - 32 x - 3 x + 32 = 0$ {factorizing left hand side}

$\Rightarrow x (3 x - 32) - 1 (3 x - 32) = 0$

$\Rightarrow 3 x - 32 = 0$ or $(x - 1) = 0$ {Zero product rule}

$\Rightarrow x = \frac{32}{3}$ or $x = 1$

Hence, the required answer is

$x =$ $\frac{32}{3}$ or $x = 1$

Suggest Corrections

Solve equations, using factorization method: 3x−22x−3=3x−8x+4

Solve equations, using factorization method:
$\frac{3 x - 2}{2 x - 3} = \frac{3 x - 8}{x + 4}$