Solve 1/3(x-8)=3x-2(x-1)+20/3

$$\frac { 1 } { 3 } ( x - 8 ) = 3 x - 2 ( x - 1 ) + \frac { 20 } { 3 }$$

Solve for x

$$x=-17$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x-8.

$$\frac{1}{3}x+\frac{1}{3}\left(-8\right)=3x-2\left(x-1\right)+\frac{20}{3}$$

Multiply \frac{1}{3} and -8 to get \frac{-8}{3}.

$$\frac{1}{3}x+\frac{-8}{3}=3x-2\left(x-1\right)+\frac{20}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{1}{3}x-\frac{8}{3}=3x-2\left(x-1\right)+\frac{20}{3}$$

Use the distributive property to multiply -2 by x-1.

$$\frac{1}{3}x-\frac{8}{3}=3x-2x+2+\frac{20}{3}$$

Combine 3x and -2x to get x.

$$\frac{1}{3}x-\frac{8}{3}=x+2+\frac{20}{3}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{1}{3}x-\frac{8}{3}=x+\frac{6}{3}+\frac{20}{3}$$

Since \frac{6}{3} and \frac{20}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x-\frac{8}{3}=x+\frac{6+20}{3}$$

Add 6 and 20 to get 26.

$$\frac{1}{3}x-\frac{8}{3}=x+\frac{26}{3}$$

Subtract x from both sides.

$$\frac{1}{3}x-\frac{8}{3}-x=\frac{26}{3}$$

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

$$-\frac{2}{3}x-\frac{8}{3}=\frac{26}{3}$$

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

$$-\frac{2}{3}x=\frac{26}{3}+\frac{8}{3}$$

Since \frac{26}{3} and \frac{8}{3} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}x=\frac{26+8}{3}$$

Add 26 and 8 to get 34.

$$-\frac{2}{3}x=\frac{34}{3}$$

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

$$x=\frac{34}{3}\left(-\frac{3}{2}\right)$$

Multiply \frac{34}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{34\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{34\left(-3\right)}{3\times 2}.

$$x=\frac{-102}{6}$$

Divide -102 by 6 to get -17.

$$x=-17$$