Solve x+2/5-x+2/6=x+2/3-x+2/10

$$\frac{ x+2 }{ 5 } - \frac{ x+2 }{ 6 } = \frac{ x+2 }{ 3 } - \frac{ x+2 }{ 10 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6,3,10.

$$6\left(x+2\right)-5\left(x+2\right)=10\left(x+2\right)-3\left(x+2\right)$$

Use the distributive property to multiply 6 by x+2.

$$6x+12-5\left(x+2\right)=10\left(x+2\right)-3\left(x+2\right)$$

Use the distributive property to multiply -5 by x+2.

$$6x+12-5x-10=10\left(x+2\right)-3\left(x+2\right)$$

Combine 6x and -5x to get x.

$$x+12-10=10\left(x+2\right)-3\left(x+2\right)$$

Subtract 10 from 12 to get 2.

$$x+2=10\left(x+2\right)-3\left(x+2\right)$$

Use the distributive property to multiply 10 by x+2.

$$x+2=10x+20-3\left(x+2\right)$$

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

$$x+2=10x+20-3x-6$$

Combine 10x and -3x to get 7x.

$$x+2=7x+20-6$$

Subtract 6 from 20 to get 14.

$$x+2=7x+14$$

Subtract 7x from both sides.

$$x+2-7x=14$$

Combine x and -7x to get -6x.

$$-6x+2=14$$

Subtract 2 from both sides.

$$-6x=14-2$$

Subtract 2 from 14 to get 12.

$$-6x=12$$

Divide both sides by -6.

$$x=\frac{12}{-6}$$

Divide 12 by -6 to get -2.

$$x=-2$$