Solve x+2/2-x+3/3=-x-4/4+x-5/5

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 2,3,4,5.

$$30\left(x+2\right)-20\left(x+3\right)=-15\left(x-4\right)+12\left(x-5\right)$$

Use the distributive property to multiply 30 by x+2.

$$30x+60-20\left(x+3\right)=-15\left(x-4\right)+12\left(x-5\right)$$

Use the distributive property to multiply -20 by x+3.

$$30x+60-20x-60=-15\left(x-4\right)+12\left(x-5\right)$$

Combine 30x and -20x to get 10x.

$$10x+60-60=-15\left(x-4\right)+12\left(x-5\right)$$

Subtract 60 from 60 to get 0.

$$10x=-15\left(x-4\right)+12\left(x-5\right)$$

Use the distributive property to multiply -15 by x-4.

$$10x=-15x+60+12\left(x-5\right)$$

Use the distributive property to multiply 12 by x-5.

$$10x=-15x+60+12x-60$$

Combine -15x and 12x to get -3x.

$$10x=-3x+60-60$$

Subtract 60 from 60 to get 0.

$$10x=-3x$$

Add 3x to both sides.

$$10x+3x=0$$

Combine 10x and 3x to get 13x.

$$13x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 13 is not equal to 0, x must be equal to 0.

$$x=0$$