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

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

Solve for x

$$x=\frac{19}{20}=0.95$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply \frac{5}{6} by 3-2x.

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

Express \frac{5}{6}\times 3 as a single fraction.

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

Multiply 5 and 3 to get 15.

$$\frac{2}{3}x-\frac{2}{3}=\frac{15}{6}+\frac{5}{6}\left(-2\right)x-x$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

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

Express \frac{5}{6}\left(-2\right) as a single fraction.

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

Multiply 5 and -2 to get -10.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}+\frac{-10}{6}x-x$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}-\frac{5}{3}x-x$$

Combine -\frac{5}{3}x and -x to get -\frac{8}{3}x.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}-\frac{8}{3}x$$

Add \frac{8}{3}x to both sides.

$$\frac{2}{3}x-\frac{2}{3}+\frac{8}{3}x=\frac{5}{2}$$

Combine \frac{2}{3}x and \frac{8}{3}x to get \frac{10}{3}x.

$$\frac{10}{3}x-\frac{2}{3}=\frac{5}{2}$$

Add \frac{2}{3} to both sides.

$$\frac{10}{3}x=\frac{5}{2}+\frac{2}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{10}{3}x=\frac{15}{6}+\frac{4}{6}$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{10}{3}x=\frac{15+4}{6}$$

Add 15 and 4 to get 19.

$$\frac{10}{3}x=\frac{19}{6}$$

Multiply both sides by \frac{3}{10}, the reciprocal of \frac{10}{3}.

$$x=\frac{19}{6}\times \frac{3}{10}$$

Multiply \frac{19}{6} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{19\times 3}{6\times 10}$$

Do the multiplications in the fraction \frac{19\times 3}{6\times 10}.

$$x=\frac{57}{60}$$

Reduce the fraction \frac{57}{60} to lowest terms by extracting and canceling out 3.

$$x=\frac{19}{20}$$