Solve {3-2/4-frac{8{2-x}}=2}

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2-x}{2-x}.

$$3-\frac{2}{\frac{4\left(2-x\right)}{2-x}-\frac{8}{2-x}}=2$$

Since \frac{4\left(2-x\right)}{2-x} and \frac{8}{2-x} have the same denominator, subtract them by subtracting their numerators.

$$3-\frac{2}{\frac{4\left(2-x\right)-8}{2-x}}=2$$

Do the multiplications in 4\left(2-x\right)-8.

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

Combine like terms in 8-4x-8.

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

Variable x cannot be equal to 2 since division by zero is not defined. Divide 2 by \frac{-4x}{2-x} by multiplying 2 by the reciprocal of \frac{-4x}{2-x}.

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

Cancel out 2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{-2x}{-2x}.

$$\frac{3\left(-2\right)x}{-2x}-\frac{-x+2}{-2x}=2$$

Since \frac{3\left(-2\right)x}{-2x} and \frac{-x+2}{-2x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-2\right)x-\left(-x+2\right)}{-2x}=2$$

Do the multiplications in 3\left(-2\right)x-\left(-x+2\right).

$$\frac{-6x+x-2}{-2x}=2$$

Combine like terms in -6x+x-2.

$$\frac{-5x-2}{-2x}=2$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by -2x.

$$-5x-2=-4x$$

Add 4x to both sides.

$$-5x-2+4x=0$$

Combine -5x and 4x to get -x.

$$-x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-x=2$$

Multiply both sides by -1.

$$x=-2$$