Solve 6+x/100+x=16/100

$$\frac { 6 + x } { 100 + x } = \frac { 16 } { 100 }$$

Solve for x

$$x = \frac{250}{21} = 11\frac{19}{21} \approx 11.904761905$$

Steps for Solving Linear Equation

Variable x cannot be equal to -100 since division by zero is not defined. Multiply both sides of the equation by 100\left(x+100\right), the least common multiple of 100+x,100.

$$100\left(6+x\right)=\left(x+100\right)\times 16$$

Use the distributive property to multiply 100 by 6+x.

$$600+100x=\left(x+100\right)\times 16$$

Use the distributive property to multiply x+100 by 16.

$$600+100x=16x+1600$$

Subtract 16x from both sides.

$$600+100x-16x=1600$$

Combine 100x and -16x to get 84x.

$$600+84x=1600$$

Subtract 600 from both sides.

$$84x=1600-600$$

Subtract 600 from 1600 to get 1000.

$$84x=1000$$

Divide both sides by 84.

$$x=\frac{1000}{84}$$

Reduce the fraction \frac{1000}{84} to lowest terms by extracting and canceling out 4.

$$x=\frac{250}{21}$$