Solve 1/a=1/6*1/x

$$\frac { 1 } { a } = \frac { 1 } { 6 } \times \frac { 1 } { x }$$

Solve for a

$$a=6x$$

$$x\neq 0$$

Solution Steps

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6ax, the least common multiple of a,6,x.

$$6x=\frac{1}{6}\times 6a\times 1$$

Multiply \frac{1}{6} and 6 to get 1.

$$6x=a\times 1$$

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

$$a\times 1=6x$$

Reorder the terms.

$$a=6x$$

Variable a cannot be equal to 0.

$$a=6x\text{, }a\neq 0$$

Solve for x

$$x=\frac{a}{6}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6ax, the least common multiple of a,6,x.

$$6x=\frac{1}{6}\times 6a\times 1$$

Multiply \frac{1}{6} and 6 to get 1.

$$6x=a\times 1$$

Reorder the terms.

$$6x=a$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{a}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{a}{6}$$

Variable x cannot be equal to 0.

$$x=\frac{a}{6}\text{, }x\neq 0$$