Question

$solve \: the \: equation \: \frac{x}{2} - 6 = 8 - \frac{2x}{3}$
​

Answer 1

Answer:

x=12

Step-by-step explanation:

$\\ \sf\longmapsto \dfrac{x}{2}-6=8-\dfrac{2x}{3}$

$\\ \sf\longmapsto \dfrac{x-12}{2}=\dfrac{24-2x}{3}$

• Using cross multiplication

$\\ \sf\longmapsto 2(24-2x)=3(x-12)$

$\\ \sf\longmapsto 48-4x=3x-36$

$\\ \sf\longmapsto 48+36=3x+4x$

$\\ \sf\longmapsto 84=7x$

$\\ \sf\longmapsto x=\dfrac{84}{7}$

$\\ \sf\longmapsto x=12$

Answer 2

Answer:

${\underline{\underline{\maltese\textbf{\textsf{\red{Question}}}}}}$

$: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bigg({8 - \dfrac{2x}{3}} \bigg)}$

$\begin{gathered}\end{gathered}$

${\underline{\underline{\maltese\textbf{\textsf{\red{Solution}}}}}}$

$: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}$

${: \implies{\sf\bigg({\dfrac{x - (6 \times 2)}{2}}\bigg) = \bf\bigg({\dfrac{(8 \times 3) - 2x}{3}} \bigg)}}$

${: \implies{\sf\bigg({\dfrac{x - 12}{2}}\bigg) = \bf\bigg({\dfrac{24 - 2x}{3}} \bigg)}}$

• By cross multiplication

$: \implies\sf{3(x - 12) = \bf{2(24 - 2x)}}$

$: \implies\sf{3x - 36 = \bf{48 - 4x}}$

$: \implies\sf{4x - 3x = \bf{48 -36}}$

$: \implies\sf{x = \bf{12}}$

${\dag{\underline{\boxed{\sf{x =12}}}}}$

• Hence, The value of x is 12.

$\begin{gathered}\end{gathered}$

${{\underline{\underline{\maltese\textbf{\textsf{\red{Verification}}}}}}}$

$: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}$

• Substituting the value of x

$: \implies{\sf\bigg({\dfrac{12}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2 \times 12}{3}} \bigg)}$

$: \implies{\sf\bigg({\dfrac{12}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{24}{3}} \bigg)}$

${: \implies{\sf\bigg({\dfrac{12 - (6 \times 2)}{2}}\bigg) = \bf\bigg({\dfrac{(8 \times 3) - 24}{3}} \bigg)}}$

${: \implies{\sf\bigg({\dfrac{12 -12}{2}}\bigg) = \bf\bigg({\dfrac{24 - 24}{3}} \bigg)}}$

${: \implies{\sf\bigg({\dfrac{0}{2}}\bigg) = \bf\bigg({\dfrac{0}{3}} \bigg)}}$

$: \implies\sf{0} = \bf{0}$

$\dag{\underline{\boxed{\sf{LHS=RHS}}}}$

Hence Verified!!