Solve 5.25/5+5+1=5.25/5-x

$$\frac{ 5.25 }{ 5+5 } +1= \frac{ 5.25 }{ 5-x }$$

Solve for x

$$x = \frac{95}{61} = 1\frac{34}{61} \approx 1.557377049$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by -x+5.

$$\left(-\frac{1}{10}x+\frac{1}{2}\right)\times 5.25-x+5=5.25$$

Use the distributive property to multiply -\frac{1}{10}x+\frac{1}{2} by 5.25.

$$-\frac{21}{40}x+\frac{21}{8}-x+5=5.25$$

Combine -\frac{21}{40}x and -x to get -\frac{61}{40}x.

$$-\frac{61}{40}x+\frac{21}{8}+5=5.25$$

Add \frac{21}{8} and 5 to get \frac{61}{8}.

$$-\frac{61}{40}x+\frac{61}{8}=5.25$$

Subtract \frac{61}{8} from both sides.

$$-\frac{61}{40}x=5.25-\frac{61}{8}$$

Subtract \frac{61}{8} from 5.25 to get -\frac{19}{8}.

$$-\frac{61}{40}x=-\frac{19}{8}$$

Multiply both sides by -\frac{40}{61}, the reciprocal of -\frac{61}{40}.

$$x=-\frac{19}{8}\left(-\frac{40}{61}\right)$$

Multiply -\frac{19}{8} and -\frac{40}{61} to get \frac{95}{61}.

$$x=\frac{95}{61}$$