Solve 3-2/4-frac{8{2-x}}=0

$$3- \frac{ 2 }{ 4- \frac{ 8 }{ 2-x } } = 0$$

Solve for x

$$x=-\frac{2}{5}=-0.4$$

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}.

$$3-\frac{2}{\frac{4\left(2-x\right)}{2-x}-\frac{8}{2-x}}=0$$

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

$$3-\frac{2}{\frac{4\left(2-x\right)-8}{2-x}}=0$$

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

$$3-\frac{2}{\frac{8-4x-8}{2-x}}=0$$

Combine like terms in 8-4x-8.

$$3-\frac{2}{\frac{-4x}{2-x}}=0$$

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}.

$$3-\frac{2\left(2-x\right)}{-4x}=0$$

Cancel out 2 in both numerator and denominator.

$$3-\frac{-x+2}{-2x}=0$$

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

$$\frac{3\left(-2\right)x}{-2x}-\frac{-x+2}{-2x}=0$$

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

$$\frac{3\left(-2\right)x-\left(-x+2\right)}{-2x}=0$$

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

$$\frac{-6x+x-2}{-2x}=0$$

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

$$\frac{-5x-2}{-2x}=0$$

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

$$-5x-2=0$$

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

$$-5x=2$$

Divide both sides by -5.

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

Fraction \frac{2}{-5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

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