Solve 4(x-5)-3x=2(x-10)-x

$$4 ( x - 5 ) - 3 x = 2 ( x - 10 ) - x$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 4 by x-5.

$$4x-20-3x=2\left(x-10\right)-x$$

Combine 4x and -3x to get x.

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

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

$$x-20=2x-20-x$$

Combine 2x and -x to get x.

$$x-20=x-20$$

Subtract x from both sides.

$$x-20-x=-20$$

Combine x and -x to get 0.

$$-20=-20$$

Compare -20 and -20.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 4 by x-5.

$$4x-20-3x=2\left(x-10\right)-x$$

Combine 4x and -3x to get x.

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

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

$$x-20=2x-20-x$$

Combine 2x and -x to get x.

$$x-20=x-20$$

Subtract x from both sides.

$$x-20-x=-20$$

Combine x and -x to get 0.

$$-20=-20$$

Compare -20 and -20.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$