Solve 3x+2-x-4/x+2-2x+1=-3/2

$$\frac{ 3x+2-x-4 }{ x+2-2x+1 } =- \frac{ 3 }{ 2 }$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-3\right), the least common multiple of x+2-2x+1,2.

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

Combine 3x and -x to get 2x.

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

Subtract 4 from 2 to get -2.

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

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

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

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

$$-4x+4=-3x+9$$

Add 3x to both sides.

$$-4x+4+3x=9$$

Combine -4x and 3x to get -x.

$$-x+4=9$$

Subtract 4 from both sides.

$$-x=9-4$$

Subtract 4 from 9 to get 5.

$$-x=5$$

Multiply both sides by -1.

$$x=-5$$