Solve 2(x-5)-3(x+3)-x=4+2(x-1)-3(1-2x)

$$2 ( x - 5 ) - 3 ( x + 3 ) - x = 4 + 2 ( x - 1 ) - 3 ( 1 - 2 x )$$

Solve for x

$$x = -\frac{9}{5} = -1\frac{4}{5} = -1.8$$

Steps for Solving Linear Equation

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

$$2x-10-3\left(x+3\right)-x=4+2\left(x-1\right)-3\left(1-2x\right)$$

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

$$2x-10-3x-9-x=4+2\left(x-1\right)-3\left(1-2x\right)$$

Combine 2x and -3x to get -x.

$$-x-10-9-x=4+2\left(x-1\right)-3\left(1-2x\right)$$

Subtract 9 from -10 to get -19.

$$-x-19-x=4+2\left(x-1\right)-3\left(1-2x\right)$$

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

$$-2x-19=4+2\left(x-1\right)-3\left(1-2x\right)$$

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

$$-2x-19=4+2x-2-3\left(1-2x\right)$$

Subtract 2 from 4 to get 2.

$$-2x-19=2+2x-3\left(1-2x\right)$$

Use the distributive property to multiply -3 by 1-2x.

$$-2x-19=2+2x-3+6x$$

Subtract 3 from 2 to get -1.

$$-2x-19=-1+2x+6x$$

Combine 2x and 6x to get 8x.

$$-2x-19=-1+8x$$

Subtract 8x from both sides.

$$-2x-19-8x=-1$$

Combine -2x and -8x to get -10x.

$$-10x-19=-1$$

Add 19 to both sides.

$$-10x=-1+19$$

Add -1 and 19 to get 18.

$$-10x=18$$

Divide both sides by -10.

$$x=\frac{18}{-10}$$

Reduce the fraction \frac{18}{-10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{9}{5}$$