Solve 2/3(6-x)-3/4(5-2x)=1/6(3-x)

$$\frac { 2 } { 3 } ( 6 - x ) - \frac { 3 } { 4 } ( 5 - 2 x ) = \frac { 1 } { 6 } ( 3 - x )$$

Solve for x

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

Steps for Solving Linear Equation

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

$$\frac{2}{3}\times 6+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

Express \frac{2}{3}\times 6 as a single fraction.

$$\frac{2\times 6}{3}+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

Multiply 2 and 6 to get 12.

$$\frac{12}{3}+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

Divide 12 by 3 to get 4.

$$4+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

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

$$4-\frac{2}{3}x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

Use the distributive property to multiply -\frac{3}{4} by 5-2x.

$$4-\frac{2}{3}x-\frac{3}{4}\times 5-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

Express -\frac{3}{4}\times 5 as a single fraction.

$$4-\frac{2}{3}x+\frac{-3\times 5}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

Multiply -3 and 5 to get -15.

$$4-\frac{2}{3}x+\frac{-15}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$4-\frac{2}{3}x-\frac{15}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

Express -\frac{3}{4}\left(-2\right) as a single fraction.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{-3\left(-2\right)}{4}x=\frac{1}{6}\left(3-x\right)$$

Multiply -3 and -2 to get 6.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{6}{4}x=\frac{1}{6}\left(3-x\right)$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{16}{4}-\frac{2}{3}x-\frac{15}{4}+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

Since \frac{16}{4} and \frac{15}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-15}{4}-\frac{2}{3}x+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

Subtract 15 from 16 to get 1.

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

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

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{6}\left(3-x\right)$$

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

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{6}\times 3+\frac{1}{6}\left(-1\right)x$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{1}{4}+\frac{5}{6}x=\frac{3}{6}+\frac{1}{6}\left(-1\right)x$$

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

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{2}+\frac{1}{6}\left(-1\right)x$$

Multiply \frac{1}{6} and -1 to get -\frac{1}{6}.

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{2}-\frac{1}{6}x$$

Add \frac{1}{6}x to both sides.

$$\frac{1}{4}+\frac{5}{6}x+\frac{1}{6}x=\frac{1}{2}$$

Combine \frac{5}{6}x and \frac{1}{6}x to get x.

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

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

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

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

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

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 2 to get 1.

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