Solve 1/2+2/5x-1/3x=7/5x+frac{1}{6}-frac{1}{3}

$$\frac { 1 } { 2 } + \frac { 2 } { 5 x } - \frac { 1 } { 3 x } = \frac { 7 } { 5 x } + \frac { 1 } { 6 } - \frac { 1 } { 3 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30x, the least common multiple of 2,5x,3x,6,3.

$$30x\times \frac{1}{2}+6\times 2-10=6\times 7+30x\times \frac{1}{6}+30x\left(-\frac{1}{3}\right)$$

Multiply 30 and \frac{1}{2} to get 15.

$$15x+6\times 2-10=6\times 7+30x\times \frac{1}{6}+30x\left(-\frac{1}{3}\right)$$

Multiply 6 and 2 to get 12.

$$15x+12-10=6\times 7+30x\times \frac{1}{6}+30x\left(-\frac{1}{3}\right)$$

Subtract 10 from 12 to get 2.

$$15x+2=6\times 7+30x\times \frac{1}{6}+30x\left(-\frac{1}{3}\right)$$

Multiply 6 and 7 to get 42.

$$15x+2=42+30x\times \frac{1}{6}+30x\left(-\frac{1}{3}\right)$$

Multiply 30 and \frac{1}{6} to get 5.

$$15x+2=42+5x+30x\left(-\frac{1}{3}\right)$$

Multiply 30 and -\frac{1}{3} to get -10.

$$15x+2=42+5x-10x$$

Combine 5x and -10x to get -5x.

$$15x+2=42-5x$$

Add 5x to both sides.

$$15x+2+5x=42$$

Combine 15x and 5x to get 20x.

$$20x+2=42$$

Subtract 2 from both sides.

$$20x=42-2$$

Subtract 2 from 42 to get 40.

$$20x=40$$

Divide both sides by 20.

$$x=\frac{40}{20}$$

Divide 40 by 20 to get 2.

$$x=2$$