Question

$\frac{x - 2}{3} - \frac{x - 3}{6} = 5 - \frac{x - 3}{18}$
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Answer 1

$\boxed{\textbf{\large{Explanation}}}$

(( x - 2 ) / 3) - ((x - 3)/ 6 ) = 5 - ((x - 3)/18 )

→ 6 ( x - 2 ) - 3 x - 3 )

= 18 ( (90 - ( x - 3 )) / 18 )

→ 6x - 12 - 3x + 9 = 90 - ( x - 3 )

→ 6x - 12 - 3x + 9 = 90 - x + 3

→ 3x - 3 = 93 - x

→ 3x + x = 93 + 3

→ 4x = 96

$\boxed{\textbf{\large{x = 24}}}$

▶for such a problems, it is very easy to find the value of x

▶ first orderly take a operations , according to the property of BODMAS

▶ Then take a values of the terms that have variable x at a one side and other constant values at a other side

▶simply do the orderly calculations then finally we can get the value of x

Answer 2

$\dfrac{x\:-\:2}{3}$ - $\dfrac{x\:-\:3}{6}$ = 5 - $\dfrac{x\:-\:3}{18}$

______________ [GIVEN]

$\implies$ $\dfrac{x\:-\:2}{3}$ - $\dfrac{x\:-\:3}{6}$ = 5 - $\dfrac{x\:-\:3}{18}$

$\implies$ $\dfrac{2x\:-\:4\:-\:x\:-\:3}{6}$ = $\dfrac{90\:-\:x\:-3}{18}$

$\implies$ $\dfrac{x\:-\:7}{6}$ = $\dfrac{87\:-\:x}{18}$

Cross-multiply them

$\implies$ 18(x - 7) = 6(87 - x)

$\implies$ 18x - 126 = 522 - 6x

$\implies$ 18x + 6x = 522 + 126

$\implies$ 24x = 648

$\implies$ x = $\dfrac{648}{24}$

______________________________

$\huge{\bold{x\:=\:27}}$

_____________ $\bold{[ANSWER]}$