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

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

Solve for x

$$x = -\frac{25}{2} = -12\frac{1}{2} = -12.5$$

Steps for Solving Linear Equation

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

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

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

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

Convert -2 to fraction -\frac{4}{2}.

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

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

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

Subtract 1 from -4 to get -5.

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

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

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

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

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

Multiply 5 and 2 to get 10.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{10}{6}$$

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

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

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

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

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

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

Add \frac{5}{2} to both sides.

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

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

$$-\frac{1}{3}x=\frac{10}{6}+\frac{15}{6}$$

Since \frac{10}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{3}x=\frac{10+15}{6}$$

Add 10 and 15 to get 25.

$$-\frac{1}{3}x=\frac{25}{6}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=\frac{25}{6}\left(-3\right)$$

Express \frac{25}{6}\left(-3\right) as a single fraction.

$$x=\frac{25\left(-3\right)}{6}$$

Multiply 25 and -3 to get -75.

$$x=\frac{-75}{6}$$

Reduce the fraction \frac{-75}{6} to lowest terms by extracting and canceling out 3.

$$x=-\frac{25}{2}$$