Solve 1/4left(x-2right)-3/47/6x=3-2x/4-frac{3left(x+4right)}{12}-x-frac{1}{3}

$$\frac{ 1 }{ 4 } \left( x-2 \right) - \frac{ 3 }{ 4 } \frac{ 7 }{ 6 } x= \frac{ 3-2x }{ 4 } - \frac{ 3 \left( x+4 \right) }{ 12 } -x- \frac{ 1 }{ 3 }$$

Solve for x

$$x=-\frac{2}{27}\approx -0.074074074$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,6,12,3.

$$3\left(x-2\right)-9\times \frac{7}{6}x=3\left(3-2x\right)-3\left(x+4\right)-12x-4$$

Use the distributive property to multiply 3 by x-2.

$$3x-6-9\times \frac{7}{6}x=3\left(3-2x\right)-3\left(x+4\right)-12x-4$$

Express 9\times \frac{7}{6} as a single fraction.

$$3x-6-\frac{9\times 7}{6}x=3\left(3-2x\right)-3\left(x+4\right)-12x-4$$

Multiply 9 and 7 to get 63.

$$3x-6-\frac{63}{6}x=3\left(3-2x\right)-3\left(x+4\right)-12x-4$$

Reduce the fraction \frac{63}{6} to lowest terms by extracting and canceling out 3.

$$3x-6-\frac{21}{2}x=3\left(3-2x\right)-3\left(x+4\right)-12x-4$$

Combine 3x and -\frac{21}{2}x to get -\frac{15}{2}x.

$$-\frac{15}{2}x-6=3\left(3-2x\right)-3\left(x+4\right)-12x-4$$

Use the distributive property to multiply 3 by 3-2x.

$$-\frac{15}{2}x-6=9-6x-3\left(x+4\right)-12x-4$$

Use the distributive property to multiply -3 by x+4.

$$-\frac{15}{2}x-6=9-6x-3x-12-12x-4$$

Combine -6x and -3x to get -9x.

$$-\frac{15}{2}x-6=9-9x-12-12x-4$$

Subtract 12 from 9 to get -3.

$$-\frac{15}{2}x-6=-3-9x-12x-4$$

Combine -9x and -12x to get -21x.

$$-\frac{15}{2}x-6=-3-21x-4$$

Subtract 4 from -3 to get -7.

$$-\frac{15}{2}x-6=-7-21x$$

Add 21x to both sides.

$$-\frac{15}{2}x-6+21x=-7$$

Combine -\frac{15}{2}x and 21x to get \frac{27}{2}x.

$$\frac{27}{2}x-6=-7$$

Add 6 to both sides.

$$\frac{27}{2}x=-7+6$$

Add -7 and 6 to get -1.

$$\frac{27}{2}x=-1$$

Multiply both sides by \frac{2}{27}, the reciprocal of \frac{27}{2}.

$$x=-\frac{2}{27}$$