Solve 1/2(3x+3)-1/3(4x-3)=1/6(5x-27)

$$\frac { 1 } { 2 } ( 3 x + 3 ) - \frac { 1 } { 3 } ( 4 x - 3 ) = \frac { 1 } { 6 } ( 5 x - 27 )$$

Solve for x

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}\times 3x+\frac{1}{2}\times 3-\frac{1}{3}\left(4x-3\right)=\frac{1}{6}\left(5x-27\right)$$

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

$$\frac{3}{2}x+\frac{1}{2}\times 3-\frac{1}{3}\left(4x-3\right)=\frac{1}{6}\left(5x-27\right)$$

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

$$\frac{3}{2}x+\frac{3}{2}-\frac{1}{3}\left(4x-3\right)=\frac{1}{6}\left(5x-27\right)$$

Use the distributive property to multiply -\frac{1}{3} by 4x-3.

$$\frac{3}{2}x+\frac{3}{2}-\frac{1}{3}\times 4x-\frac{1}{3}\left(-3\right)=\frac{1}{6}\left(5x-27\right)$$

Express -\frac{1}{3}\times 4 as a single fraction.

$$\frac{3}{2}x+\frac{3}{2}+\frac{-4}{3}x-\frac{1}{3}\left(-3\right)=\frac{1}{6}\left(5x-27\right)$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{3}{2}x+\frac{3}{2}-\frac{4}{3}x-\frac{1}{3}\left(-3\right)=\frac{1}{6}\left(5x-27\right)$$

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

$$\frac{3}{2}x+\frac{3}{2}-\frac{4}{3}x+\frac{-\left(-3\right)}{3}=\frac{1}{6}\left(5x-27\right)$$

Multiply -1 and -3 to get 3.

$$\frac{3}{2}x+\frac{3}{2}-\frac{4}{3}x+\frac{3}{3}=\frac{1}{6}\left(5x-27\right)$$

Divide 3 by 3 to get 1.

$$\frac{3}{2}x+\frac{3}{2}-\frac{4}{3}x+1=\frac{1}{6}\left(5x-27\right)$$

Combine \frac{3}{2}x and -\frac{4}{3}x to get \frac{1}{6}x.

$$\frac{1}{6}x+\frac{3}{2}+1=\frac{1}{6}\left(5x-27\right)$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{6}x+\frac{3}{2}+\frac{2}{2}=\frac{1}{6}\left(5x-27\right)$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}x+\frac{3+2}{2}=\frac{1}{6}\left(5x-27\right)$$

Add 3 and 2 to get 5.

$$\frac{1}{6}x+\frac{5}{2}=\frac{1}{6}\left(5x-27\right)$$

Use the distributive property to multiply \frac{1}{6} by 5x-27.

$$\frac{1}{6}x+\frac{5}{2}=\frac{1}{6}\times 5x+\frac{1}{6}\left(-27\right)$$

Multiply \frac{1}{6} and 5 to get \frac{5}{6}.

$$\frac{1}{6}x+\frac{5}{2}=\frac{5}{6}x+\frac{1}{6}\left(-27\right)$$

Multiply \frac{1}{6} and -27 to get \frac{-27}{6}.

$$\frac{1}{6}x+\frac{5}{2}=\frac{5}{6}x+\frac{-27}{6}$$

Reduce the fraction \frac{-27}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}x+\frac{5}{2}=\frac{5}{6}x-\frac{9}{2}$$

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

$$\frac{1}{6}x+\frac{5}{2}-\frac{5}{6}x=-\frac{9}{2}$$

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

$$-\frac{2}{3}x+\frac{5}{2}=-\frac{9}{2}$$

Subtract \frac{5}{2} from both sides.

$$-\frac{2}{3}x=-\frac{9}{2}-\frac{5}{2}$$

Since -\frac{9}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x=\frac{-9-5}{2}$$

Subtract 5 from -9 to get -14.

$$-\frac{2}{3}x=\frac{-14}{2}$$

Divide -14 by 2 to get -7.

$$-\frac{2}{3}x=-7$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

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

Express -7\left(-\frac{3}{2}\right) as a single fraction.

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

Multiply -7 and -3 to get 21.

$$x=\frac{21}{2}$$