Solve 2(x-1/3)+7/6-x=3(1/2-x)

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

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

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

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

Express 2\left(-\frac{1}{3}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Least common multiple of 3 and 6 is 6. Convert -\frac{2}{3} and \frac{7}{6} to fractions with denominator 6.

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

Since -\frac{4}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

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

Add -4 and 7 to get 3.

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

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

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

Combine 2x and -x to get x.

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

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

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

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

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

Add 3x to both sides.

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

Combine x and 3x to get 4x.

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

Subtract \frac{1}{2} from both sides.

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

Since \frac{3}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 3 to get 2.

$$4x=\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$4x=1$$

Divide both sides by 4.

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