Solve 2x+3x+9=8(6-x)(R:3)

$$2 x + 3 x + 9 = 8 ( 6 - x ) ( R : 3 )$$

Solve for R

$$R=-\frac{3\left(5x+9\right)}{8\left(x-6\right)}$$

$$x\neq 6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$6x+9x+27=8\left(6-x\right)R$$

Combine 6x and 9x to get 15x.

$$15x+27=8\left(6-x\right)R$$

Use the distributive property to multiply 8 by 6-x.

$$15x+27=\left(48-8x\right)R$$

Use the distributive property to multiply 48-8x by R.

$$15x+27=48R-8xR$$

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

$$48R-8xR=15x+27$$

Combine all terms containing R.

$$\left(48-8x\right)R=15x+27$$

Divide both sides by 48-8x.

$$\frac{\left(48-8x\right)R}{48-8x}=\frac{15x+27}{48-8x}$$

Dividing by 48-8x undoes the multiplication by 48-8x.

$$R=\frac{15x+27}{48-8x}$$

Divide 15x+27 by 48-8x.

$$R=\frac{3\left(5x+9\right)}{8\left(6-x\right)}$$

Solve for x

$$x=-\frac{3\left(9-16R\right)}{8R+15}$$

$$R\neq -\frac{15}{8}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$6x+9x+27=8\left(6-x\right)R$$

Combine 6x and 9x to get 15x.

$$15x+27=8\left(6-x\right)R$$

Use the distributive property to multiply 8 by 6-x.

$$15x+27=\left(48-8x\right)R$$

Use the distributive property to multiply 48-8x by R.

$$15x+27=48R-8xR$$

Add 8xR to both sides.

$$15x+27+8xR=48R$$

Subtract 27 from both sides.

$$15x+8xR=48R-27$$

Combine all terms containing x.

$$\left(15+8R\right)x=48R-27$$

The equation is in standard form.

$$\left(8R+15\right)x=48R-27$$

Divide both sides by 15+8R.

$$\frac{\left(8R+15\right)x}{8R+15}=\frac{48R-27}{8R+15}$$

Dividing by 15+8R undoes the multiplication by 15+8R.

$$x=\frac{48R-27}{8R+15}$$

Divide 48R-27 by 15+8R.

$$x=\frac{3\left(16R-9\right)}{8R+15}$$