Solve 50/x+50=110/210

$$\frac { 50 } { x + 50 } = \frac { 110 } { 210 }$$

Solve for x

$$x = \frac{500}{11} = 45\frac{5}{11} \approx 45.454545455$$

Steps for Solving Linear Equation

Variable x cannot be equal to -50 since division by zero is not defined. Multiply both sides of the equation by 210\left(x+50\right), the least common multiple of x+50,210.

$$210\times 50=\left(x+50\right)\times 110$$

Multiply 210 and 50 to get 10500.

$$10500=\left(x+50\right)\times 110$$

Use the distributive property to multiply x+50 by 110.

$$10500=110x+5500$$

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

$$110x+5500=10500$$

Subtract 5500 from both sides.

$$110x=10500-5500$$

Subtract 5500 from 10500 to get 5000.

$$110x=5000$$

Divide both sides by 110.

$$x=\frac{5000}{110}$$

Reduce the fraction \frac{5000}{110} to lowest terms by extracting and canceling out 10.

$$x=\frac{500}{11}$$