Answer:
[tex]\qquad\qquad\qquad\boxed{ \sf{ \: \bf \: x = 11 \: }} \\ \\ [/tex]
Step-by-step explanation:
Given linear equation is
[tex]\sf \:\dfrac{x + 2}{6} - \left(\dfrac{11 - x}{3} - \dfrac{1}{4}\right) = \dfrac{3x - 4}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{x + 2}{6} - \left(\dfrac{4(11 - x) - 3}{12}\right) = \dfrac{3x - 4}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{x + 2}{6} -\dfrac{44 - 4x - 3}{12} = \dfrac{3x - 4}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{x + 2}{6} -\dfrac{41 - 4x}{12} = \dfrac{3x - 4}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{2(x + 2) - (41 - 4x)}{12} = \dfrac{3x - 4}{12} \\ \\ [/tex]
[tex]\sf \:2x + 4 - 41 + 4x = 3x - 4 \\ \\ [/tex]
[tex]\sf \:6x - 37 = 3x - 4 \\ \\ [/tex]
[tex]\sf \:6x - 3x = 37 - 4 \\ \\ [/tex]
[tex]\sf \: 3x = 33 \\ \\ [/tex]
[tex]\sf\implies \bf \: x = 11 \\ \\ [/tex]
Verification
Given linear equation is
[tex]\sf \:\dfrac{11 + 2}{6} - \left(\dfrac{11 - 11}{3} - \dfrac{1}{4}\right) = \dfrac{3(11) - 4}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{13}{6} - \left( - \dfrac{1}{4}\right) = \dfrac{33 - 4}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{13}{6} + \dfrac{1}{4} = \dfrac{29}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{26 + 3}{12} = \dfrac{29}{12} \\ \\ [/tex]
[tex]\sf \:\dfrac{29}{12} = \dfrac{29}{12} \\ \\ [/tex]
Hence, Verified