Solve x+3/2-2x-4/8=x-2-2x/4

$$\frac { x + 3 } { 2 } - \frac { 2 x - 4 } { 8 } = x - \frac { 2 - 2 x } { 4 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 2,8,4.

$$4\left(x+3\right)-\left(2x-4\right)=8x-2\left(2-2x\right)$$

Use the distributive property to multiply 4 by x+3.

$$4x+12-\left(2x-4\right)=8x-2\left(2-2x\right)$$

To find the opposite of 2x-4, find the opposite of each term.

$$4x+12-2x-\left(-4\right)=8x-2\left(2-2x\right)$$

The opposite of -4 is 4.

$$4x+12-2x+4=8x-2\left(2-2x\right)$$

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

$$2x+12+4=8x-2\left(2-2x\right)$$

Add 12 and 4 to get 16.

$$2x+16=8x-2\left(2-2x\right)$$

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

$$2x+16=8x-4+4x$$

Combine 8x and 4x to get 12x.

$$2x+16=12x-4$$

Subtract 12x from both sides.

$$2x+16-12x=-4$$

Combine 2x and -12x to get -10x.

$$-10x+16=-4$$

Subtract 16 from both sides.

$$-10x=-4-16$$

Subtract 16 from -4 to get -20.

$$-10x=-20$$

Divide both sides by -10.

$$x=\frac{-20}{-10}$$

Divide -20 by -10 to get 2.

$$x=2$$