Question

simplify the following: x/2-14(x-1/3)=18(x+1)+1/12​

Answer 1

GIVEN :–

$\\ \implies \sf \dfrac{x}{2} - 14 \left(x - \dfrac{1}{3} \right) = 18(x + 1) + \dfrac{1}{12}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \implies \sf \dfrac{x}{2} - 14 \left(x - \dfrac{1}{3} \right) = 18(x + 1) + \dfrac{1}{12}$

$\\ \implies \sf \dfrac{x}{2} - 14x + \left( \dfrac{14}{3} \right) = 18x + 18 + \dfrac{1}{12}$

$\\ \implies \sf \dfrac{x}{2} - 14x - 18x= 18 + \dfrac{1}{12} - \left( \dfrac{14}{3} \right)$

$\\ \implies \sf \dfrac{x}{2} - 32x= \dfrac{217}{12} - \left( \dfrac{14}{3} \right)$

$\\ \implies \sf - \dfrac{63x}{2} = \dfrac{217 - 56}{12}$

$\\ \implies \sf - \dfrac{63x}{2} = \dfrac{161}{12}$

$\\ \implies \sf -63x = \dfrac{161}{6}$

$\\ \implies \sf -9x = \dfrac{23}{6}$

$\\ \implies \sf -x = \dfrac{23}{54}$

$\\ \implies \large { \boxed{ \sf x = - \dfrac{23}{54}}}$

Answer 2

$\mathfrak {\underline{\orange{Answer}}}$

$\begin{lgathered}\\ \sf \dfrac{x}{2} - 14 \left(x - \dfrac{1}{3} \right) = 18(x + 1) + \dfrac{1}{12} \\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} \dfrac{x}{2} - 14x + \left( \dfrac{14}{3} \right) = 18x + 18 + \dfrac{1}{12} \\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} \dfrac{x}{2} - 14x - 18x= 18 + \dfrac{1}{12} - \left( \dfrac{14}{3} \right)\\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} \dfrac{x}{2} - 32x= \dfrac{217}{12} - \left( \dfrac{14}{3} \right)\\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} - \dfrac{63x}{2} = \dfrac{217 - 56}{12}\\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} - \dfrac{63x}{2} = \dfrac{161}{12}\\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} -63x = \dfrac{161}{6}\\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} -9x = \dfrac{23}{6}\\\end{lgathered}$

$\begin{lgathered}\\ \sf \red{⇝} -x = \dfrac{23}{54}\\\end{lgathered}$

$\begin{lgathered}\\ \sf \therefore \large { \orange{ x = \dfrac{-23}{54}}}\\\end{lgathered}$

Your answer = -23/54