Solve t6:t8=7:9quadt9:t13:2

$$t 6 : t 8 = 7 : 9 \quad t 9 : t 13 : 2$$

Solve for t_13

$$\left\{\begin{matrix}t_{13}=\frac{7t_{8}t_{9}}{18t_{6}}\text{, }&t_{9}\neq 0\text{ and }t_{8}\neq 0\text{ and }t_{6}\neq 0\\t_{13}\neq 0\text{, }&t_{6}=0\text{ and }t_{9}=0\text{ and }t_{8}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2t_{8}, the least common multiple of t_{8},2.

$$2t_{6}=t_{8}\times \frac{\frac{7}{9}t_{9}}{t_{13}}$$

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

$$t_{8}\times \frac{\frac{7}{9}t_{9}}{t_{13}}=2t_{6}$$

Variable t_{13} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by t_{13}.

$$t_{8}\times \frac{7}{9}t_{9}=2t_{6}t_{13}$$

Reorder the terms.

$$\frac{7}{9}t_{8}t_{9}=2t_{6}t_{13}$$

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

$$2t_{6}t_{13}=\frac{7}{9}t_{8}t_{9}$$

The equation is in standard form.

$$2t_{6}t_{13}=\frac{7t_{8}t_{9}}{9}$$

Divide both sides by 2t_{6}.

$$\frac{2t_{6}t_{13}}{2t_{6}}=\frac{7t_{8}t_{9}}{9\times 2t_{6}}$$

Dividing by 2t_{6} undoes the multiplication by 2t_{6}.

$$t_{13}=\frac{7t_{8}t_{9}}{9\times 2t_{6}}$$

Divide \frac{7t_{8}t_{9}}{9} by 2t_{6}.

$$t_{13}=\frac{7t_{8}t_{9}}{18t_{6}}$$

Variable t_{13} cannot be equal to 0.

$$t_{13}=\frac{7t_{8}t_{9}}{18t_{6}}\text{, }t_{13}\neq 0$$

Solve for t_6

$$t_{6}=\frac{7t_{8}t_{9}}{18t_{13}}$$

$$t_{8}\neq 0\text{ and }t_{13}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2t_{8}, the least common multiple of t_{8},2.

$$2t_{6}=t_{8}\times \frac{\frac{7}{9}t_{9}}{t_{13}}$$

Multiply both sides of the equation by t_{13}.

$$2t_{6}t_{13}=t_{8}\times \frac{7}{9}t_{9}$$

Reorder the terms.

$$2t_{6}t_{13}=\frac{7}{9}t_{8}t_{9}$$

The equation is in standard form.

$$2t_{13}t_{6}=\frac{7t_{8}t_{9}}{9}$$

Divide both sides by 2t_{13}.

$$\frac{2t_{13}t_{6}}{2t_{13}}=\frac{7t_{8}t_{9}}{9\times 2t_{13}}$$

Dividing by 2t_{13} undoes the multiplication by 2t_{13}.

$$t_{6}=\frac{7t_{8}t_{9}}{9\times 2t_{13}}$$

Divide \frac{7t_{8}t_{9}}{9} by 2t_{13}.

$$t_{6}=\frac{7t_{8}t_{9}}{18t_{13}}$$