Solve x-45/55 x-47/53=x-55/45 x-53/47

Question

Solve the equation

x = - \frac{1485}{2491}

Alternative Form

x \approx - 0.596146

Evaluate

x - \frac{45}{55} x - \frac{47}{53} = x - \frac{55}{45} x - \frac{53}{47}

Cancel equal terms on both sides of the expression

- \frac{45}{55} x - \frac{47}{53} = - \frac{55}{45} x - \frac{53}{47}

Cancel out the common factor 5

- \frac{9}{11} x - \frac{47}{53} = - \frac{55}{45} x - \frac{53}{47}

Cancel out the common factor 5

- \frac{9}{11} x - \frac{47}{53} = - \frac{11}{9} x - \frac{53}{47}

Multiply both sides of the equation by LCM

(- \frac{9}{11} x - \frac{47}{53}) \times 246609 = (- \frac{11}{9} x - \frac{53}{47}) \times 246609

Calculate

More Steps

- 201771 x - 218691 = (- \frac{11}{9} x - \frac{53}{47}) \times 246609

Calculate

More Steps

- 201771 x - 218691 = - 301411 x - 278091

Move the expression to the left side

- 201771 x - 218691 + 301411 x = - 278091

Move the expression to the right side

- 201771 x + 301411 x = - 278091 + 218691

Add and subtract

More Steps

99640 x = - 278091 + 218691

Add and subtract

99640 x = - 59400

Divide both sides

\frac{99640 x}{99640} = \frac{- 59400}{99640}

Divide the numbers

x = \frac{- 59400}{99640}

Solution

More Steps

x = - \frac{1485}{2491}

Alternative Form

x \approx - 0.596146

Show Solution

2491 x = - 1485

Show Solution