Question

2x/3 – x/2 = 30 solve the following equation and check ​

Answer 1

Answer:

$\sf \: \frac{2x}{3} - \frac{x}{2} = 30$

$\sf \: \frac{4x -3x }{6} = 30$

$\sf \: \frac{x}{6} = 30$

$\sf \: x= 30 \times 6$

$\sf \: x= 180$

Hope it help.

Answer 2

Given :

• $\sf{ \dfrac{2x}{3} - \dfrac{x}{2} = 30 }$

To Find :

• Solve it and Check the Answer

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\maltese \; {\underline{\textbf{\textsf{ Solving \; the \; Equation \; :- }}}}$

$\longmapsto$ We have the Equation :

$\qquad \dashrightarrow \; {\underline{\boxed {\pmb{\sf { \dfrac{2x}{3} - \dfrac{x}{2} = 30 }}}}}$

$\longmapsto$ LCM of 3 and 2 is 6 :

$\qquad \dashrightarrow \; {\underline{\boxed {\pmb{\sf { \dfrac{2x}{6} - \dfrac{x}{6} = 30 }}}}}$

$\longmapsto$ So the Value of Numerator will be :

$\qquad \dashrightarrow \; {\underline{\boxed {\pmb{\sf { \dfrac{4x}{6} - \dfrac{3x}{6} = 30 }}}}}$

$\longmapsto$ On Subtracting we have :

$\qquad \dashrightarrow \; {\underline{\boxed {\pmb{\sf { \dfrac{x}{6} = 30 }}}}}$

$\longmapsto$ Transporting 6 to RHS Side :

$\qquad \dashrightarrow \; {\underline{\boxed {\pmb{\sf { x = 30 \times 6 }}}}}$

$\longmapsto$ We get the Answer :

$\qquad \dashrightarrow \; {\underline{\boxed {\pmb{\sf { x = 180 }}}}} \; {\red{\bigstar}}$

$\maltese \; {\underline{\textbf{\textsf{ Checking \; the \; Answer \; :- }}}}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{2x}{3} - \dfrac{x}{2} = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{ ( 2 \times 180) }{3} - \dfrac{180}{2} = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{ 360 }{3} - \dfrac{180}{2} = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{ 360 }{6} - \dfrac{180}{6} = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{ 360 - 180 }{6} = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{ 180 }{6} = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \cancel\dfrac{ 180 }{6} = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 30 = 30 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ LHS = RHS }}}}} \; {\purple{\bigstar}} \\ \\ \\ \end{gathered}$

HENCE , VERIFIED ...!!

$\therefore \;$ Required Answer is 180 .

$\\ \qquad{\rule{200pt}{2pt}}$