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

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

Solve for x

$$x = \frac{57}{25} = 2\frac{7}{25} = 2.28$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-3.

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

Combine 2x and x to get 3x.

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

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

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

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$3x-6=\frac{1}{3}+\frac{2}{9}x$$

Subtract \frac{2}{9}x from both sides.

$$3x-6-\frac{2}{9}x=\frac{1}{3}$$

Combine 3x and -\frac{2}{9}x to get \frac{25}{9}x.

$$\frac{25}{9}x-6=\frac{1}{3}$$

Add 6 to both sides.

$$\frac{25}{9}x=\frac{1}{3}+6$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{25}{9}x=\frac{1}{3}+\frac{18}{3}$$

Since \frac{1}{3} and \frac{18}{3} have the same denominator, add them by adding their numerators.

$$\frac{25}{9}x=\frac{1+18}{3}$$

Add 1 and 18 to get 19.

$$\frac{25}{9}x=\frac{19}{3}$$

Multiply both sides by \frac{9}{25}, the reciprocal of \frac{25}{9}.

$$x=\frac{19}{3}\times \frac{9}{25}$$

Multiply \frac{19}{3} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{19\times 9}{3\times 25}$$

Do the multiplications in the fraction \frac{19\times 9}{3\times 25}.

$$x=\frac{171}{75}$$

Reduce the fraction \frac{171}{75} to lowest terms by extracting and canceling out 3.

$$x=\frac{57}{25}$$