Solve 6/R-8=4(8Q+1)

$$\frac { 6 } { R - 8 } = 4 ( 8 Q + 1 )$$

Solve for Q

$$Q=-\frac{19-2R}{16\left(8-R\right)}$$

$$R\neq 8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R-8.

$$6=4\left(8Q+1\right)\left(R-8\right)$$

Use the distributive property to multiply 4 by 8Q+1.

$$6=\left(32Q+4\right)\left(R-8\right)$$

Use the distributive property to multiply 32Q+4 by R-8.

$$6=32QR-256Q+4R-32$$

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

$$32QR-256Q+4R-32=6$$

Subtract 4R from both sides.

$$32QR-256Q-32=6-4R$$

Add 32 to both sides.

$$32QR-256Q=6-4R+32$$

Add 6 and 32 to get 38.

$$32QR-256Q=38-4R$$

Combine all terms containing Q.

$$\left(32R-256\right)Q=38-4R$$

Divide both sides by 32R-256.

$$\frac{\left(32R-256\right)Q}{32R-256}=\frac{38-4R}{32R-256}$$

Dividing by 32R-256 undoes the multiplication by 32R-256.

$$Q=\frac{38-4R}{32R-256}$$

Divide 38-4R by 32R-256.

$$Q=\frac{19-2R}{16\left(R-8\right)}$$

Solve for R

$$R=\frac{128Q+19}{2\left(8Q+1\right)}$$

$$Q\neq -\frac{1}{8}$$

Steps for Solving Linear Equation

Variable R cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by R-8.

$$6=4\left(8Q+1\right)\left(R-8\right)$$

Use the distributive property to multiply 4 by 8Q+1.

$$6=\left(32Q+4\right)\left(R-8\right)$$

Use the distributive property to multiply 32Q+4 by R-8.

$$6=32QR-256Q+4R-32$$

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

$$32QR-256Q+4R-32=6$$

Add 256Q to both sides.

$$32QR+4R-32=6+256Q$$

Add 32 to both sides.

$$32QR+4R=6+256Q+32$$

Add 6 and 32 to get 38.

$$32QR+4R=38+256Q$$

Combine all terms containing R.

$$\left(32Q+4\right)R=38+256Q$$

The equation is in standard form.

$$\left(32Q+4\right)R=256Q+38$$

Divide both sides by 32Q+4.

$$\frac{\left(32Q+4\right)R}{32Q+4}=\frac{256Q+38}{32Q+4}$$

Dividing by 32Q+4 undoes the multiplication by 32Q+4.

$$R=\frac{256Q+38}{32Q+4}$$

Divide 38+256Q by 32Q+4.

$$R=\frac{128Q+19}{2\left(8Q+1\right)}$$

Variable R cannot be equal to 8.

$$R=\frac{128Q+19}{2\left(8Q+1\right)}\text{, }R\neq 8$$