Solve (1/3(5x-3)+1/2(1-x)=1/4(x-2)

$$( \frac { 1 } { 3 } ( 5 x - 3 ) + \frac { 1 } { 2 } ( 1 - x ) = \frac { 1 } { 4 } ( x - 2 )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 5x-3.

$$\frac{1}{3}\times 5x+\frac{1}{3}\left(-3\right)+\frac{1}{2}\left(1-x\right)=\frac{1}{4}\left(x-2\right)$$

Multiply \frac{1}{3} and 5 to get \frac{5}{3}.

$$\frac{5}{3}x+\frac{1}{3}\left(-3\right)+\frac{1}{2}\left(1-x\right)=\frac{1}{4}\left(x-2\right)$$

Multiply \frac{1}{3} and -3 to get \frac{-3}{3}.

$$\frac{5}{3}x+\frac{-3}{3}+\frac{1}{2}\left(1-x\right)=\frac{1}{4}\left(x-2\right)$$

Divide -3 by 3 to get -1.

$$\frac{5}{3}x-1+\frac{1}{2}\left(1-x\right)=\frac{1}{4}\left(x-2\right)$$

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

$$\frac{5}{3}x-1+\frac{1}{2}+\frac{1}{2}\left(-1\right)x=\frac{1}{4}\left(x-2\right)$$

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

$$\frac{5}{3}x-1+\frac{1}{2}-\frac{1}{2}x=\frac{1}{4}\left(x-2\right)$$

Convert -1 to fraction -\frac{2}{2}.

$$\frac{5}{3}x-\frac{2}{2}+\frac{1}{2}-\frac{1}{2}x=\frac{1}{4}\left(x-2\right)$$

Since -\frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}x+\frac{-2+1}{2}-\frac{1}{2}x=\frac{1}{4}\left(x-2\right)$$

Add -2 and 1 to get -1.

$$\frac{5}{3}x-\frac{1}{2}-\frac{1}{2}x=\frac{1}{4}\left(x-2\right)$$

Combine \frac{5}{3}x and -\frac{1}{2}x to get \frac{7}{6}x.

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

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

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

Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.

$$\frac{7}{6}x-\frac{1}{2}=\frac{1}{4}x+\frac{-2}{4}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{7}{6}x-\frac{1}{2}=\frac{1}{4}x-\frac{1}{2}$$

Subtract \frac{1}{4}x from both sides.

$$\frac{7}{6}x-\frac{1}{2}-\frac{1}{4}x=-\frac{1}{2}$$

Combine \frac{7}{6}x and -\frac{1}{4}x to get \frac{11}{12}x.

$$\frac{11}{12}x-\frac{1}{2}=-\frac{1}{2}$$

Add \frac{1}{2} to both sides.

$$\frac{11}{12}x=-\frac{1}{2}+\frac{1}{2}$$

Add -\frac{1}{2} and \frac{1}{2} to get 0.

$$\frac{11}{12}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since \frac{11}{12} is not equal to 0, x must be equal to 0.

$$x=0$$