Question

solve the equation...
​

Answer 1

Answer :

The required value of x is -6/19

Step-by-step explanation :

Given :

$\sf \dfrac{x}{6}+3(x+1)=2$

To find :

the value of x

Solution :

  $\sf \dfrac{x}{6}+3(x+1)=2 \\\\ \sf \dfrac{x}{6}+3x + 3=2 \\\\ \sf \dfrac{x}{6}+3x=2-3 \\\\ \sf \dfrac{x}{6}+3x=-1$

LCM = 6

  $\sf \dfrac{x}{6}+\bigg(3x \times \dfrac{6}{6}\bigg)=-1 \\\\ \sf \dfrac{x}{6}+\dfrac{18x}{6}=-1 \\\\ \sf \dfrac{x+18x}{6}=-1 \\\\ \sf \dfrac{19x}{6}=-1 \\\\ \sf 19x=-1 \times 6 \\\\ \sf 19x=-6 \\\\ \sf x=\dfrac{-6}{19}$

The required value of x is -6/19

Verification :

Put x = -6/19,

$\sf \dfrac{x}{6}+3(x+1)=2 \\\\ \sf \dfrac{\dfrac{-6}{19}}{6}+3\bigg(\dfrac{-6}{19}+1\bigg)=2 \\\\ \sf \dfrac{-6}{6 \times 19} +3\bigg(\dfrac{-6+19}{19}\bigg)=2 \\\\ \sf \dfrac{-1}{19}+3\bigg(\dfrac{13}{19}\bigg)=2 \\\\ \sf \dfrac{-1}{19}+\dfrac{39}{19}=2 \\\\ \sf \dfrac{-1+39}{19}=2 \\\\ \sf \dfrac{38}{19}=2 \\\\ \sf \dfrac{19 \times 2}{19}=2 \\\\ \sf 2=2 \\\\ \rm LHS=RHS$

Hence verified!

Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➙ The value of x is $\sf-\frac{6}{19}$ ${\boxed{\green{\checkmark{}}}}$

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

Given equation :

$\sf \frac{x}{6} + 3(x + 1) = 2$

Solving for x :

$\sf : \implies \frac{x}{6} + 3(x + 1) = 2$

$\sf : \implies \frac{x}{6} + 3x + 3 = 2$

$\sf : \implies \frac{x + 18x + 18}{6} = 2$

$\sf : \implies \frac{19x + 18}{6} = 2$

$\sf : \implies 19x + 18 = 12$

$\sf : \implies 19x = 12 - 18$

$\sf : \implies 19x = - 6$

$\sf : \green{ \implies x = \frac{ - 6}{19} }$

${{\underline{\underline{{\textsf{\textbf{Check point : }}}}}}}$

$: \sf \implies \frac{x}{6} + 3(x + 1) = 2$

$: \sf \implies \frac{ \frac{ - 6}{19} }{6} + 3 \bigg( \frac{ - 6}{19} + 1 \bigg) = 2$

$: \sf \implies \frac{ - 6}{19 \times 6} + 3 \bigg( \frac{ - 6 + 19}{19} \bigg) = 2$

$: \sf \implies \frac{ - 1}{19} + 3 \bigg( \frac{13}{19} \bigg) = 2$

$: \sf \implies \frac{ - 1}{19} + \frac{39}{19} = 2$

$: \sf \implies \frac{ - 1 + 39}{19} = 2$

$: \sf \implies \frac{38}{19} = 2$

$: \sf \implies 2 = 2$

As we getting L. H. S. = R. H. S.

Hence proved ${\boxed{\green{\checkmark{}}}}$