Solve 2/7-1/5x+2/3x=x-4/3-frac{x}{5}

$$\frac { 2 } { 7 } - \frac { 1 } { 5 } x + \frac { 2 } { 3 } x = x - \frac { 4 } { 3 } - \frac { x } { 5 }$$

Solve for x

$$x = \frac{34}{7} = 4\frac{6}{7} \approx 4.857142857$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 105, the least common multiple of 7,5,3.

$$30-21x+70x=105x-140-21x$$

Combine -21x and 70x to get 49x.

$$30+49x=105x-140-21x$$

Combine 105x and -21x to get 84x.

$$30+49x=84x-140$$

Subtract 84x from both sides.

$$30+49x-84x=-140$$

Combine 49x and -84x to get -35x.

$$30-35x=-140$$

Subtract 30 from both sides.

$$-35x=-140-30$$

Subtract 30 from -140 to get -170.

$$-35x=-170$$

Divide both sides by -35.

$$x=\frac{-170}{-35}$$

Reduce the fraction \frac{-170}{-35} to lowest terms by extracting and canceling out -5.

$$x=\frac{34}{7}$$