Solve 2/3(4x-1)-(2x-17x/3)=1/3x+4/3

$$\frac { 2 } { 3 } ( 4 x - 1 ) - ( 2 x - \frac { 17 x } { 3 } ) = \frac { 1 } { 3 } x + \frac { 4 } { 3 }$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$2\left(4x-1\right)-3\left(2x-\frac{17x}{3}\right)=1x+4$$

Use the distributive property to multiply 2 by 4x-1.

$$8x-2-3\left(2x-\frac{17x}{3}\right)=1x+4$$

Subtract 1x from both sides.

$$8x-2-3\left(2x-\frac{17x}{3}\right)-x=4$$

Multiply both sides of the equation by 3.

$$3\left(8x-2-3\left(2x-\frac{17x}{3}\right)\right)-3x=12$$

Multiply both sides of the equation by 3.

$$9\left(8x-2-3\left(2x-\frac{17x}{3}\right)\right)-9x=36$$

Use the distributive property to multiply -3 by 2x-\frac{17x}{3}.

$$9\left(8x-2-6x+3\times \frac{17x}{3}\right)-9x=36$$

Express 3\times \frac{17x}{3} as a single fraction.

$$9\left(8x-2-6x+\frac{3\times 17x}{3}\right)-9x=36$$

Cancel out 3 and 3.

$$9\left(8x-2-6x+17x\right)-9x=36$$

Combine -6x and 17x to get 11x.

$$9\left(8x-2+11x\right)-9x=36$$

Combine 8x and 11x to get 19x.

$$9\left(19x-2\right)-9x=36$$

Use the distributive property to multiply 9 by 19x-2.

$$171x-18-9x=36$$

Combine 171x and -9x to get 162x.

$$162x-18=36$$

Add 18 to both sides.

$$162x=36+18$$

Add 36 and 18 to get 54.

$$162x=54$$

Divide both sides by 162.

$$x=\frac{54}{162}$$

Reduce the fraction \frac{54}{162} to lowest terms by extracting and canceling out 54.

$$x=\frac{1}{3}$$