Question

Solve:-
$\sf{\dfrac{6x+1}{3}+1=\dfrac{x - 3}{6}}$​

Answer 1

Given Equation:-

• $\sf{\dfrac{6x+1}{3}+1=\dfrac{x - 3}{6}}$

⠀

Solution:-

★ Multiplying both sides of the equation by 6,

$\tt\longmapsto{\dfrac{6(6x + 1)}{3}+ 6 × 1 =\dfrac{6(x - 3)}{6}}$

$\tt\longmapsto{2(6x + 1) + 6 = x - 3}$

⠀⠀$\boxed{\sf{\purple{(Opening\: the\: brackets)}}}$

$\large{\tt\longmapsto{12x + 2 + 6 = x - 3}}$

$\large{\tt\longmapsto{12x + 8 = x - 3}}$

$\large{\tt\longmapsto{12x - x + 8 = -3}}$

$\large{\tt\longmapsto{11x + 8 = -3}}$

$\large{\tt\longmapsto{11x = -3 - 8}}$

$\large{\tt\longmapsto{11x = -11}}$

$\large{\boxed{\tt{\longmapsto{\orange{x = -1}}}}}$

⠀

Verification:-

$\large{\tt{\longmapsto{L.H.S =\dfrac{6(-1)+ 1}{3}}}}$

$\large{\tt{\longmapsto{\dfrac{-6 + 1}{3}+ 1}}}$

$\large{\tt{\longmapsto{\dfrac{-5}{3} +\dfrac{3}{3}}}}$

$\large{\tt{\longmapsto{\dfrac{-5 + 3}{3} = \dfrac{-2}{3}}}}$

$\large{\tt{\longmapsto{R.H.S =\dfrac{(-1)- 3}{6} =\dfrac{-4}{6} =\dfrac{-2}{3}}}}$

⠀⠀⠀⠀⠀$\large{\boxed{\sf{\green{L.H.S\: =\: R.H.S}}}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬