Solve 16.1V=18.8R/{R_{1}+21Omega}

$$16.1V = 18.8 \frac{ R }{ { R }_{ 1 } +21 \Omega }$$

Solve for R

$$R=V\times \frac{161R_{1}+3381\Omega }{188}$$

$$R_{1}\neq -21\Omega$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{1}+21\Omega .

$$16.1V\left(R_{1}+21\Omega \right)=18.8R$$

Use the distributive property to multiply 16.1V by R_{1}+21\Omega .

$$16.1VR_{1}+338.1\Omega V=18.8R$$

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

$$18.8R=16.1VR_{1}+338.1\Omega V$$

The equation is in standard form.

$$18.8R=\frac{161R_{1}V+3381V\Omega }{10}$$

Divide both sides of the equation by 18.8, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{18.8R}{18.8}=\frac{V\times \frac{161R_{1}+3381\Omega }{10}}{18.8}$$

Dividing by 18.8 undoes the multiplication by 18.8.

$$R=\frac{V\times \frac{161R_{1}+3381\Omega }{10}}{18.8}$$

Divide V\times \frac{161R_{1}+3381\Omega }{10} by 18.8 by multiplying V\times \frac{161R_{1}+3381\Omega }{10} by the reciprocal of 18.8.

$$R=\frac{161V\left(R_{1}+21\Omega \right)}{188}$$

Solve for R_1

$$\left\{\begin{matrix}R_{1}=-21\Omega +\frac{188R}{161V}\text{, }&R\neq 0\text{ and }V\neq 0\\R_{1}\neq -21\Omega \text{, }&V=0\text{ and }R=0\end{matrix}\right.$$