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

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

Solve for x

$$x=\frac{3}{8}=0.375$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Use the distributive property to multiply \frac{1}{4} by \frac{2}{3}x-\frac{1}{6}.

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

Multiply \frac{1}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 2}{4\times 3}.

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

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{1}{4} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 6}.

$$\frac{1}{2}x+\frac{1}{6}+\frac{1}{6}x+\frac{-1}{24}=x$$

Fraction \frac{-1}{24} can be rewritten as -\frac{1}{24} by extracting the negative sign.

$$\frac{1}{2}x+\frac{1}{6}+\frac{1}{6}x-\frac{1}{24}=x$$

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

$$\frac{2}{3}x+\frac{1}{6}-\frac{1}{24}=x$$

Least common multiple of 6 and 24 is 24. Convert \frac{1}{6} and \frac{1}{24} to fractions with denominator 24.

$$\frac{2}{3}x+\frac{4}{24}-\frac{1}{24}=x$$

Since \frac{4}{24} and \frac{1}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}x+\frac{4-1}{24}=x$$

Subtract 1 from 4 to get 3.

$$\frac{2}{3}x+\frac{3}{24}=x$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}x+\frac{1}{8}=x$$

Subtract x from both sides.

$$\frac{2}{3}x+\frac{1}{8}-x=0$$

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

$$-\frac{1}{3}x+\frac{1}{8}=0$$

Subtract \frac{1}{8} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{3}x=-\frac{1}{8}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=-\frac{1}{8}\left(-3\right)$$

Express -\frac{1}{8}\left(-3\right) as a single fraction.

$$x=\frac{-\left(-3\right)}{8}$$

Multiply -1 and -3 to get 3.

$$x=\frac{3}{8}$$