Solve frac{a_{11}}{a_{18}}=2/3Rightarrowa+10/a+17d=2/3=

$$\frac { a _ { 11 } } { a _ { 18 } } = \frac { 2 } { 3 } \Rightarrow \frac { a + 10 } { a + 17 d } = \frac { 2 } { 3 } =$$

Solve for a_11

$$a_{11}=\frac{2a_{18}}{3}$$

$$a_{18}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3a_{18}, the least common multiple of a_{18},3.

$$3a_{11}=2a_{18}$$

Divide both sides by 3.

$$\frac{3a_{11}}{3}=\frac{2a_{18}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$a_{11}=\frac{2a_{18}}{3}$$

Solve for a_18

$$a_{18}=\frac{3a_{11}}{2}$$

$$a_{11}\neq 0$$

Steps for Solving Linear Equation

Variable a_{18} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3a_{18}, the least common multiple of a_{18},3.

$$3a_{11}=2a_{18}$$

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

$$2a_{18}=3a_{11}$$

Divide both sides by 2.

$$\frac{2a_{18}}{2}=\frac{3a_{11}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a_{18}=\frac{3a_{11}}{2}$$

Variable a_{18} cannot be equal to 0.

$$a_{18}=\frac{3a_{11}}{2}\text{, }a_{18}\neq 0$$