Question

$5x - 2(2x - y ) = 2(3x - 1) + \frac{7}{2}$​

Answer 1

$\large\star\underline\textsf{Correct Question :- }$

$\underbrace{\sf{\purple{5x-2(2x-7)=2(3x-1)+ \dfrac{7}{2} }}}$

$\red{\underbrace{\mathtt{Ans. \dfrac{5}{2} }}}$

$\huge\underline\textsf{Explantion:- }$

$\small{\underline{\overline{\mid{\mathsf{\purple{\:\: Let \:open\: the \:brackets\:\:} \mid}}}}}$

$\leadsto\sf LHS = 5x - 4x + 14 = x + 14$

$\leadsto\sf RHS = 6x - 2 + \dfrac{7}{2}$

$\leadsto\sf6x - \dfrac{4}{2} + \dfrac{7}{2}$

$\leadsto\sf6x + \dfrac{3}{2}$

$\leadsto\sf The \: equation \: is \: x + 14 = 6x + \dfrac{3}{2}$

$\leadsto\sf14 = 6x - x + \dfrac{3}{2 }$

$\leadsto\sf14 = 5x + \dfrac{3}{2}$

$\underbrace{\sf\bigg(Transposing \: \dfrac{3}{2} \bigg) }$

$\leadsto\sf14 - \dfrac{3}{2} = 5x$

$\leadsto\sf \dfrac{28 - 3}{2} = 5x$

$\leadsto\sf \dfrac{25}{2} = 5x$

$\leadsto\sf x = \dfrac{25}{2 } \times \dfrac{1}{5} = \dfrac{5 \times 5}{2 \times 5}$

$\leadsto\boxed{\sf x = \dfrac{5}{2} }$

$\underbrace{\sf Therefore ,\: requried \: solution \: is \: x = \dfrac{5}{2} }$

$\huge\underline{\underline{\texttt{\purple{Verification-}}}}$

$\implies\sf \: LHS \: = 5 \times \dfrac{5}{2} - 2\bigg( \dfrac{5}{2} \times 2 - 7\bigg)$

$\implies\sf \dfrac{25}{2} - 2\bigg(5 - 7\bigg)$

$\implies\sf \dfrac{25}{2} - 2\bigg( - 2\bigg)$

$\implies\sf \dfrac{25}{2} + 4$

$\implies\sf \dfrac{25 + 8}{2}$

$\implies\sf \dfrac{33}{2}$

$\implies\sf RHS = 2\bigg( \dfrac{5}{2} \times 3 - 1\bigg) + \dfrac{7}{2}$

$\implies\sf2\bigg( \dfrac{15}{2} - \dfrac{2}{2} \bigg) + \dfrac{7}{2}$

$\implies\sf \dfrac{2 \times 13}{2} + \dfrac{7}{2}$

$\implies\sf \dfrac{26 + 7}{2}$

$\implies\sf \dfrac{33}{2} = LHS$

Answer 2

$5x - 2(2x - y ) = 2(3x - 1) + \frac{7}{2} \\ \\ = > 5x -( 4x - 2y) = (6x - 2) + \frac{7}{2} \\ \\ = > 5x - 4x + 2y = 6x - 2 + \frac{7}{2} \\ \\ = > x + 2y = 6x - \frac{( (- 4) + 7)}{2} \\ \\ = > x + 2y = 6x + \frac{3}{2} \\ \\ = > x - 6x = \frac{3}{2} - 2y \\ \\ = > ( - 5x )= \frac{3}{2} - 2y \\ \\ = > x = ( \frac{3}{2} - 2y) \div ( - 5) \\ \\ = > x = (\frac{3}{2} \div ( - 5)) - (2y \div ( - 5)) \\ \\ = > x = (( - \frac{3}{2} ) \div 5) +( 2y \div 5) \\ \\ = > x = (( - \frac{3}{2}) \times \frac{1}{5} ) + \frac{2}{5}y \\ \\ = > x = \frac{( - 3 \times 1)}{(2 \times 5)} + \frac{2}{5}y \\ \\ = > \green{ \boxed{ x = - \frac{3}{10} + \frac{2}{5}y }} \\ \\=>\green{ \boxed{y= \frac{5}{2}x + \frac{3}{4}}}$