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

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

Solve for x

$$x=\frac{1}{23}\approx 0.043478261$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by \frac{1}{3}-x.

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

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

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

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

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

Use the distributive property to multiply \frac{1}{3} by x-\frac{1}{2}.

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

Multiply \frac{1}{3} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{3\times 2}.

$$\frac{1}{6}-\frac{1}{2}x+\frac{1}{3}x+\frac{-1}{6}=\frac{1}{6}-4x$$

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

$$\frac{1}{6}-\frac{1}{2}x+\frac{1}{3}x-\frac{1}{6}=\frac{1}{6}-4x$$

Combine -\frac{1}{2}x and \frac{1}{3}x to get -\frac{1}{6}x.

$$\frac{1}{6}-\frac{1}{6}x-\frac{1}{6}=\frac{1}{6}-4x$$

Subtract \frac{1}{6} from \frac{1}{6} to get 0.

$$-\frac{1}{6}x=\frac{1}{6}-4x$$

Add 4x to both sides.

$$-\frac{1}{6}x+4x=\frac{1}{6}$$

Combine -\frac{1}{6}x and 4x to get \frac{23}{6}x.

$$\frac{23}{6}x=\frac{1}{6}$$

Multiply both sides by \frac{6}{23}, the reciprocal of \frac{23}{6}.

$$x=\frac{1}{6}\times \frac{6}{23}$$

Multiply \frac{1}{6} times \frac{6}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\times 6}{6\times 23}$$

Cancel out 6 in both numerator and denominator.

$$x=\frac{1}{23}$$