Solve -x-(x-1)/5=x-2/2-3/5

$$\frac { - x - ( x - 1 ) } { 5 } = \frac { x - 2 } { 2 } - \frac { 3 } { 5 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,2.

$$2\left(-x-\left(x-1\right)\right)=5\left(x-2\right)-6$$

To find the opposite of x-1, find the opposite of each term.

$$2\left(-x-x-\left(-1\right)\right)=5\left(x-2\right)-6$$

The opposite of -1 is 1.

$$2\left(-x-x+1\right)=5\left(x-2\right)-6$$

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

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

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

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

Subtract 6 from -10 to get -16.

$$2\left(-x\right)-2x+2=5x-16$$

Subtract 5x from both sides.

$$2\left(-x\right)-2x+2-5x=-16$$

Combine -2x and -5x to get -7x.

$$2\left(-x\right)-7x+2=-16$$

Subtract 2 from both sides.

$$2\left(-x\right)-7x=-16-2$$

Subtract 2 from -16 to get -18.

$$2\left(-x\right)-7x=-18$$

Multiply 2 and -1 to get -2.

$$-2x-7x=-18$$

Combine -2x and -7x to get -9x.

$$-9x=-18$$

Divide both sides by -9.

$$x=\frac{-18}{-9}$$

Divide -18 by -9 to get 2.

$$x=2$$