Solve 3/4m=mg-m100/R

$$\frac { 3 } { 4 } m = m g - m \frac { 100 } { R }$$

Solve for R

$$\left\{\begin{matrix}R=-\frac{400}{3-4g}\text{, }&g\neq \frac{3}{4}\\R\neq 0\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4R, the least common multiple of 4,R.

$$\frac{3}{4}m\times 4R=mg\times 4R-m\times 4\times 100$$

Multiply \frac{3}{4} and 4 to get 3.

$$3mR=mg\times 4R-m\times 4\times 100$$

Multiply 4 and 100 to get 400.

$$3mR=mg\times 4R-m\times 400$$

Subtract mg\times 4R from both sides.

$$3mR-mg\times 4R=-m\times 400$$

Multiply -1 and 400 to get -400.

$$3mR-mg\times 4R=-400m$$

Multiply -1 and 4 to get -4.

$$3mR-4mgR=-400m$$

Combine all terms containing R.

$$\left(3m-4mg\right)R=-400m$$

The equation is in standard form.

$$\left(3m-4gm\right)R=-400m$$

Divide both sides by 3m-4mg.

$$\frac{\left(3m-4gm\right)R}{3m-4gm}=-\frac{400m}{3m-4gm}$$

Dividing by 3m-4mg undoes the multiplication by 3m-4mg.

$$R=-\frac{400m}{3m-4gm}$$

Divide -400m by 3m-4mg.

$$R=-\frac{400}{3-4g}$$

Variable R cannot be equal to 0.

$$R=-\frac{400}{3-4g}\text{, }R\neq 0$$

Solve for g

$$\left\{\begin{matrix}g=\frac{3}{4}+\frac{100}{R}\text{, }&R\neq 0\\g\in \mathrm{R}\text{, }&m=0\text{ and }R\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4R, the least common multiple of 4,R.

$$\frac{3}{4}m\times 4R=mg\times 4R-m\times 4\times 100$$

Multiply \frac{3}{4} and 4 to get 3.

$$3mR=mg\times 4R-m\times 4\times 100$$

Multiply 4 and 100 to get 400.

$$3mR=mg\times 4R-m\times 400$$

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

$$mg\times 4R-m\times 400=3mR$$

Add m\times 400 to both sides.

$$mg\times 4R=3mR+m\times 400$$

The equation is in standard form.

$$4Rmg=3Rm+400m$$

Divide both sides by 4mR.

$$\frac{4Rmg}{4Rm}=\frac{m\left(3R+400\right)}{4Rm}$$

Dividing by 4mR undoes the multiplication by 4mR.

$$g=\frac{m\left(3R+400\right)}{4Rm}$$

Divide m\left(400+3R\right) by 4mR.

$$g=\frac{3}{4}+\frac{100}{R}$$