Solve 100=6x(5+5*R/4)+5*R

$$100 = 6 x ( 5 + \frac { 5 \cdot R } { 4 } ) + 5 \cdot R$$

Solve for R

$$R=-\frac{4\left(3x-10\right)}{3x+2}$$

$$x\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$400=24x\left(5+\frac{5R}{4}\right)+20R$$

Use the distributive property to multiply 24x by 5+\frac{5R}{4}.

$$400=120x+24x\times \frac{5R}{4}+20R$$

Cancel out 4, the greatest common factor in 24 and 4.

$$400=120x+6\times 5Rx+20R$$

Multiply 6 and 5 to get 30.

$$400=120x+30Rx+20R$$

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

$$120x+30Rx+20R=400$$

Subtract 120x from both sides.

$$30Rx+20R=400-120x$$

Combine all terms containing R.

$$\left(30x+20\right)R=400-120x$$

Divide both sides by 30x+20.

$$\frac{\left(30x+20\right)R}{30x+20}=\frac{400-120x}{30x+20}$$

Dividing by 30x+20 undoes the multiplication by 30x+20.

$$R=\frac{400-120x}{30x+20}$$

Divide 400-120x by 30x+20.

$$R=\frac{4\left(10-3x\right)}{3x+2}$$

Solve for x

$$x=-\frac{2\left(R-20\right)}{3\left(R+4\right)}$$

$$R\neq -4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$400=24x\left(5+\frac{5R}{4}\right)+20R$$

Use the distributive property to multiply 24x by 5+\frac{5R}{4}.

$$400=120x+24x\times \frac{5R}{4}+20R$$

Cancel out 4, the greatest common factor in 24 and 4.

$$400=120x+6\times 5Rx+20R$$

Multiply 6 and 5 to get 30.

$$400=120x+30Rx+20R$$

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

$$120x+30Rx+20R=400$$

Subtract 20R from both sides.

$$120x+30Rx=400-20R$$

Combine all terms containing x.

$$\left(120+30R\right)x=400-20R$$

The equation is in standard form.

$$\left(30R+120\right)x=400-20R$$

Divide both sides by 120+30R.

$$\frac{\left(30R+120\right)x}{30R+120}=\frac{400-20R}{30R+120}$$

Dividing by 120+30R undoes the multiplication by 120+30R.

$$x=\frac{400-20R}{30R+120}$$

Divide 400-20R by 120+30R.

$$x=\frac{2\left(20-R\right)}{3\left(R+4\right)}$$