Solve 3{1-[1-2(1-x)]}=-2(x-2)

$$3 \{ 1 - [ 1 - 2 ( 1 - x ) ] \} = - 2 ( x - 2 )$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

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

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

Subtract 2 from 1 to get -1.

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

To find the opposite of -1+2x, find the opposite of each term.

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

The opposite of -1 is 1.

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

Add 1 and 1 to get 2.

$$3\left(2-2x\right)=-2\left(x-2\right)$$

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

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

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

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

Add 2x to both sides.

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

Combine -6x and 2x to get -4x.

$$6-4x=4$$

Subtract 6 from both sides.

$$-4x=4-6$$

Subtract 6 from 4 to get -2.

$$-4x=-2$$

Divide both sides by -4.

$$x=\frac{-2}{-4}$$

Reduce the fraction \frac{-2}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{1}{2}$$