Solve 10-1/x-1=50-4/10-4

$$\frac { 10 - 1 } { x - 1 } = \frac { 50 - 4 } { 10 - 4 }$$

Solve for x

$$x = \frac{50}{23} = 2\frac{4}{23} \approx 2.173913043$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$10-1=\left(\frac{1}{6}x-\frac{1}{6}\right)\left(50-4\right)$$

Subtract 1 from 10 to get 9.

$$9=\left(\frac{1}{6}x-\frac{1}{6}\right)\left(50-4\right)$$

Subtract 4 from 50 to get 46.

$$9=\left(\frac{1}{6}x-\frac{1}{6}\right)\times 46$$

Use the distributive property to multiply \frac{1}{6}x-\frac{1}{6} by 46.

$$9=\frac{23}{3}x-\frac{23}{3}$$

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

$$\frac{23}{3}x-\frac{23}{3}=9$$

Add \frac{23}{3} to both sides.

$$\frac{23}{3}x=9+\frac{23}{3}$$

Add 9 and \frac{23}{3} to get \frac{50}{3}.

$$\frac{23}{3}x=\frac{50}{3}$$

Multiply both sides by \frac{3}{23}, the reciprocal of \frac{23}{3}.

$$x=\frac{50}{3}\times \frac{3}{23}$$

Multiply \frac{50}{3} and \frac{3}{23} to get \frac{50}{23}.

$$x=\frac{50}{23}$$