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Transposing Method

Identify the ...

Question

Identify the equations below, which has no solution?

\frac{3}{8} (x - 2) = \frac{8}{3} (x + 2)

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- \frac{3}{2} (2 x - 8) = 3 x - 12

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4 (\frac{3}{4} x + 5) = 3 x + 20

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6 (\frac{2}{3} x + 5) = 4 x + 5

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Solution

The correct option is B $6 (\frac{2}{3} x + 5) = 4 x + 5$
(A) $\frac{3}{8} (x - 2) = \frac{8}{3} (x + 2)$
$\Rightarrow 9 (x - 2) = 64 (x + 2)$
$\Rightarrow 9 x - 18 = 64 x + 128$
$\Rightarrow 9 x - 64 x = 128 + 18$
$\Rightarrow - 55 x = 146$
$\Rightarrow x = \frac{- 146}{55}$

(B) $- \frac{3}{2} (2 x - 8) = 3 x - 12$
$\Rightarrow - 3 (2 x - 8) = 6 x - 24$
$\Rightarrow - 6 x + 24 = 6 x + 24$
$\Rightarrow - 6 x - 6 x = - 24 - 24$
$\Rightarrow - 12 x = - 48$
$\Rightarrow x = 4$

(C) $(\frac{3}{4} x + 5) = 2 x + 20$
$\Rightarrow 3 x + 5 = 2 x + 20$
$\Rightarrow 3 x - 2 x = 20 - 5$
$\Rightarrow x = 15$

(D) $6 (\frac{2}{3} x + 5) = (4 x + 5)$
$\Rightarrow \frac{12 x}{3} x + 30 = 4 x + 5$
$\Rightarrow 4 x + 30 = 4 x + 5$
$4 x - 4 x = 5 - 30$ this is not possible

In these equation A,B,C, has solution
But equation D has no solution

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Similar questions

4 x^{5} + 7 x^{4} + 14 x^{3} + 3 x^{2} - 8 x + 6

x^{2} + 3 x + 2

Solve the equations:

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(vi) 6x + 1 = 3(x − 1) + 7;

(vii) ;

(viii) ;

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(xi) 6(1 − 4x) + 7(2 + 5x) = 53;

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(xiv) .

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2

x^{6} - 3 x^{5} + 4 x^{3} + 3 x^{2} + 4 = 0

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