Solve 3[2x+1-2(2x-1)]+4=2[1+2(3-x)]

$$3 [ 2 x + 1 - 2 ( 2 x - 1 ) ] + 4 = 2 [ 1 + 2 ( 3 - x ) ]$$

Solve for x

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

Steps for Solving Linear Equation

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

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

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

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

Add 1 and 2 to get 3.

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

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

$$-6x+9+4=2\left(1+2\left(3-x\right)\right)$$

Add 9 and 4 to get 13.

$$-6x+13=2\left(1+2\left(3-x\right)\right)$$

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

$$-6x+13=2\left(1+6-2x\right)$$

Add 1 and 6 to get 7.

$$-6x+13=2\left(7-2x\right)$$

Use the distributive property to multiply 2 by 7-2x.

$$-6x+13=14-4x$$

Add 4x to both sides.

$$-6x+13+4x=14$$

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

$$-2x+13=14$$

Subtract 13 from both sides.

$$-2x=14-13$$

Subtract 13 from 14 to get 1.

$$-2x=1$$

Divide both sides by -2.

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

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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