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

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

Solve for x

$$x = -\frac{17}{6} = -2\frac{5}{6} \approx -2.833333333$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

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

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

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

Since -\frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -4 to get -7.

$$-\frac{1}{6}x-\frac{7}{6}=\frac{5}{6}\left(x+2\right)$$

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

$$-\frac{1}{6}x-\frac{7}{6}=\frac{5}{6}x+\frac{5}{6}\times 2$$

Express \frac{5}{6}\times 2 as a single fraction.

$$-\frac{1}{6}x-\frac{7}{6}=\frac{5}{6}x+\frac{5\times 2}{6}$$

Multiply 5 and 2 to get 10.

$$-\frac{1}{6}x-\frac{7}{6}=\frac{5}{6}x+\frac{10}{6}$$

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

$$-\frac{1}{6}x-\frac{7}{6}=\frac{5}{6}x+\frac{5}{3}$$

Subtract \frac{5}{6}x from both sides.

$$-\frac{1}{6}x-\frac{7}{6}-\frac{5}{6}x=\frac{5}{3}$$

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

$$-x-\frac{7}{6}=\frac{5}{3}$$

Add \frac{7}{6} to both sides.

$$-x=\frac{5}{3}+\frac{7}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{5}{3} and \frac{7}{6} to fractions with denominator 6.

$$-x=\frac{10}{6}+\frac{7}{6}$$

Since \frac{10}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$-x=\frac{10+7}{6}$$

Add 10 and 7 to get 17.

$$-x=\frac{17}{6}$$

Multiply both sides by -1.

$$x=-\frac{17}{6}$$