Solve 4/x-4=-5

$$\frac { 4 } { x - 4 } = - 5$$

Solve for x

$$x = \frac{16}{5} = 3\frac{1}{5} = 3.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.

$$4=-5\left(x-4\right)$$

Use the distributive property to multiply -5 by x-4.

$$4=-5x+20$$

Swap sides so that all variable terms are on the left hand side.

$$-5x+20=4$$

Subtract 20 from both sides.

$$-5x=4-20$$

Subtract 20 from 4 to get -16.

$$-5x=-16$$

Divide both sides by -5.

$$x=\frac{-16}{-5}$$

Fraction \frac{-16}{-5} can be simplified to \frac{16}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{16}{5}$$