Solve 2*(1-3x^-1)^-1-5=1

$$2 \cdot ( 1 - 3 x ^ { - 1 } ) ^ { - 1 } - 5 = 1$$

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Add 5 to both sides.

$$2\left(1-3x^{-1}\right)^{-1}=1+5$$

Add 1 and 5 to get 6.

$$2\left(1-3x^{-1}\right)^{-1}=6$$

Divide both sides by 2.

$$\left(1-3x^{-1}\right)^{-1}=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$\left(1-3x^{-1}\right)^{-1}=3$$

Reorder the terms.

$$\frac{1}{1-3\times \frac{1}{x}}=3$$

Express -3\times \frac{1}{x} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

Since \frac{x}{x} and \frac{-3}{x} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{x-3}{x}}=3$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 1 by \frac{x-3}{x} by multiplying 1 by the reciprocal of \frac{x-3}{x}.

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

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

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

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

$$x=3x-9$$

Subtract 3x from both sides.

$$x-3x=-9$$

Combine x and -3x to get -2x.

$$-2x=-9$$

Divide both sides by -2.

$$x=\frac{-9}{-2}$$

Fraction \frac{-9}{-2} can be simplified to \frac{9}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{2}$$