Question

solve this equation :- 1/5(2x+1) - 1/3 (x-2)=x - 24⅓. only for moderators and stars.
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Answer 1

$\tt \qquad : \implies\: \dfrac{1}{5} \: (2x + 1) - \dfrac{1}{3} \: (x - 2) = x - (24) \: \dfrac{1}{3}$

$\qquad \tt : \implies \: \dfrac{2x + 1}{5} - \dfrac{x - 2}{3} = x - ( 24) \: \cancel \dfrac{1}{ 3}$

$\qquad \tt : \implies \: \dfrac{3 \: (2x + 1) - 3 \: (x - 2)}{15} = x - 8$

$\qquad {\sf : \implies \: \because \: LCM \: of \: 5 \: and \: 3 \: is \: 15.}$

$\qquad \tt : \implies \: \dfrac{6x + 1 - 3x + 2}{15} = x - 8$

$\tt \qquad : \implies \: \dfrac{6x - 3x + 1 + 2}{15} = x - 8$

$\tt\qquad : \implies \: \dfrac{3x + 3}{15} = x - 8$

$\tt \qquad : \implies \: \dfrac{3 \: (x + 1)}{3 \: (5)} = x - 8$

$\tt \qquad : \implies \: \dfrac{ \cancel3 \: (x + 1)}{ \cancel3 \: (5)} = \dfrac{x - 8}{1}$

$\tt \qquad : \implies \: \dfrac{x + 1}{5} = \dfrac{x - 8}{1}$

$\tt \qquad : \implies \: x + 1 = 5 \: (x - 8)$

$\tt \qquad : \implies \: x + 1 = 5x - 40$

$\tt \qquad : \implies \: x - 5x = - 40 - 1$

$\tt \qquad : \implies \: - 4x = - 41$

$\tt \qquad : \implies \: x = \dfrac{41}{4}$

$\qquad :\implies\large{ \sf~Verification :}$

${\sf \qquad : \implies \: Taking ~ the \: simplest \: form \: of \: the \: equation : }$

$\tt \qquad : \implies \: x + 1 = 5x - 40$

$\tt \qquad: \implies \: \bigg \lgroup \dfrac{ 41}{4} \bigg \rgroup + 1 = 5 \: \bigg \lgroup \dfrac{41}{4} \bigg \rgroup - 40$

$\tt \qquad : \implies \: \dfrac{41 + 4}{4} = \dfrac{205}{4} - 40$

$\tt \qquad : \implies \: \dfrac{45}{4} = \dfrac{205 - 160}{4}$

$\tt \qquad : \implies \: \dfrac{45}{4} = \dfrac{45}{4}$

${\sf \qquad : \implies \: Hence, \: verified!}$