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

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

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply 5 by x-1.

$$5x-5-\left(1-x\right)=2\left(x-1\right)-4\left(1-x\right)$$

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

$$5x-5-1-\left(-x\right)=2\left(x-1\right)-4\left(1-x\right)$$

The opposite of -x is x.

$$5x-5-1+x=2\left(x-1\right)-4\left(1-x\right)$$

Subtract 1 from -5 to get -6.

$$5x-6+x=2\left(x-1\right)-4\left(1-x\right)$$

Combine 5x and x to get 6x.

$$6x-6=2\left(x-1\right)-4\left(1-x\right)$$

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

$$6x-6=2x-2-4\left(1-x\right)$$

Use the distributive property to multiply -4 by 1-x.

$$6x-6=2x-2-4+4x$$

Subtract 4 from -2 to get -6.

$$6x-6=2x-6+4x$$

Combine 2x and 4x to get 6x.

$$6x-6=6x-6$$

Subtract 6x from both sides.

$$6x-6-6x=-6$$

Combine 6x and -6x to get 0.

$$-6=-6$$

Compare -6 and -6.

$$\text{true}$$

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 5 by x-1.

$$5x-5-\left(1-x\right)=2\left(x-1\right)-4\left(1-x\right)$$

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

$$5x-5-1-\left(-x\right)=2\left(x-1\right)-4\left(1-x\right)$$

The opposite of -x is x.

$$5x-5-1+x=2\left(x-1\right)-4\left(1-x\right)$$

Subtract 1 from -5 to get -6.

$$5x-6+x=2\left(x-1\right)-4\left(1-x\right)$$

Combine 5x and x to get 6x.

$$6x-6=2\left(x-1\right)-4\left(1-x\right)$$

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

$$6x-6=2x-2-4\left(1-x\right)$$

Use the distributive property to multiply -4 by 1-x.

$$6x-6=2x-2-4+4x$$

Subtract 4 from -2 to get -6.

$$6x-6=2x-6+4x$$

Combine 2x and 4x to get 6x.

$$6x-6=6x-6$$

Subtract 6x from both sides.

$$6x-6-6x=-6$$

Combine 6x and -6x to get 0.

$$-6=-6$$

Compare -6 and -6.

$$\text{true}$$

This is true for any x.

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