Solve 2(6-2x)/3-x=4

$$\frac{ 2(6-2x) }{ 3-x } =4$$

Solve for x

$$x\neq 3$$

Solution Steps

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by -x+3.

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

Use the distributive property to multiply 2 by 6-2x.

$$12-4x=4\left(-x+3\right)$$

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

$$12-4x=-4x+12$$

Add 4x to both sides.

$$12-4x+4x=12$$

Combine -4x and 4x to get 0.

$$12=12$$

Compare 12 and 12.

$$\text{true}$$

This is true for any x.

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

Variable x cannot be equal to 3.

$$x\in \mathrm{R}\setminus 3$$