Question

$\frac{2x - 1}{3} = \frac{x - 2}{3}$
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Answer 1

$\qquad : \implies \: \bold{\dfrac{2x - 1}{3} = \dfrac{x - 2}{3} }$

$\:$

$\bf\qquad : \implies \: {3 \: (2x - 1) = 3 \: (x - 2)}$

$\:$

$\bf \qquad : \implies \: 6x - 3 = 3x - 6$

$\:$

$\qquad : \implies \: \bf6x - 3x = - 6 + 3$

$\:$

$\bf \qquad : \implies \: 3x = - 3$

$\:$

$\bf \qquad : \implies \: x = \cancel\dfrac{ - 3}{3}$

$\:$

$\bf \qquad : \implies \: x = - 1$

$\qquad$ V E R I F I C A T I O N :

$\:$

$\:$

$\bf\qquad : \implies \: \dfrac{2x - 1}{3} = \dfrac{x - 2}{3}$

$\:$

$\bf \qquad : \implies \: \dfrac{2( - 1) - 1}{3} = \dfrac{ - 1 - 2}{3}$

$\:$

$\bf \qquad : \implies \: \dfrac{ - 2 - 1}{3} = \dfrac{ - 3}{3}$

$\:$

$\bf \qquad : \implies \: \dfrac{ - 3}{3} = \dfrac{ - 3}{3}$

$\:$

$\qquad$ LHS = RHS

$~$

$\qquad$ HENCE, VERIFIED!