Isolate the variable to one side.

Multiply each side by $\displaystyle \frac{2}{3}$:

$\displaystyle \frac{x}{\frac{2}{3}}=6$

$\displaystyle \frac{x\frac{2}{3}}{\frac{2}{3}}=\frac{6}{1}*\frac{2}{3}$

Simplify and reduce:

$\displaystyle x=4$

The goal is to isolate the variable on one side.

$\displaystyle \frac{x}{\frac{4}{5}} = 2$

The opposite operation of division is multiplication, therefore , multiply each side by $\displaystyle \frac{4}{5}$:

$\displaystyle \frac{\frac{4}{5}x}{\frac{4}{5}} = \frac{4}{5}\times 2$

The left hand side can be reduced by recalling that anything divided by itself is equal to 1:

$\displaystyle 1\times x = \frac{4}{5} \times 2$

The identity law of multiplication takes effect and we get the solution as:

$\displaystyle x = \frac{8}{5}$

The goal is to isolate the variable on one side.

$\displaystyle \frac{6}{7} x = 3$

The opposite operation of multiplication is division, therefore, we can either divide each side by $\displaystyle \frac{6}{7}$ or multiply each side by its reciprocal $\displaystyle \frac{7}{6}$:

$\displaystyle \frac{7}{6}\times \frac{6}{7}x = \frac{7}{6}\times 3$

The left hand side can be reduced by recalling that anything multiplying a fraction by its reciprocal is equal to 1:

$\displaystyle 1\times x = \frac{7}{6} \times 3$

The identity law of multiplication takes effect and we get the solution as:

$\displaystyle x = \frac{21}{6}$

However, this solution can be reduced by dividing both the numerator and denominator by 3:

$\displaystyle x = \frac{7}{2}$

The goal is to isolate the variable on one side.

$\displaystyle x + \frac{7}{3} = \frac{1}{6}$

The opposite operation of addition is subtraction so subtract $\displaystyle \frac{7}{3}$ from each side:

$\displaystyle x + \frac{7}{3} - \frac{7}{3} = \frac{1}{6} - \frac{7}{3}$

In order to complete the subtraction on the right hand side, we must first determine the common denominator, or common multiples of 3 and 6. The least common multiple of 3 and 6 is 6 itself.

$\displaystyle x = \frac{1}{6} - \frac{14}{6}$

Simplifying, we get the final solution:

$\displaystyle x = -\frac{13}{6}$

The goal is to isolate the variable on one side.

$\displaystyle x - \frac{5}{6} = \frac{5}{12}$

The opposite operation of subtraction is addition so add $\displaystyle \frac{5}{6}$ to each side:

$\displaystyle x - \frac{5}{6} + \frac{5}{6} = \frac{5}{12} + \frac{5}{6}$

In order to complete the addition on the right hand side, we must first determine the common denominator, or common multiples of 6 and 12. The least common multiple of 6 and 12 is 12 itself.

$\displaystyle x = \frac{5}{12} + \frac{10}{12}$

Simplifying, we obtain the solution:

$\displaystyle x = \frac{15}{12}$

Reducing the fraction to its simplest terms we get the final solution:

$\displaystyle x = \frac{5}{4}$

To get y by itself, you must divide by 6 on both sides

$\displaystyle \frac{6y}{6}=\frac{15}{6}$

which simplifies to

$\displaystyle y=\frac{15}{6}=\frac{5}{2}$

To get x by itself, you must multiply both sides of the equation by 5

$\displaystyle \frac{x}{5}\times5=\frac{1}{3}\times5$

which simplifies to

$\displaystyle x=\frac{5}{3}$

For this equation, isolate the variable $\displaystyle \small x$ by preforming equivalent operations on both sides of the equation.

To isolate a variable multiplied by a fraction, any fraction multiplied by it's reciprocal equals one. 

$\displaystyle \small \left(\frac{5}{1}\right)\small \frac{1}{5}x=5\left(\frac{5}{1}\right)$

Because $\displaystyle \small \frac{5}{5} = 1$, we isolate $\displaystyle \small x$, and the equation becomes $\displaystyle \small x=5\cdot \left(\frac{5}{1}\right)$

multiplying the values on the right side gives us

$\displaystyle \small x=\frac{25}{1}= 25$

$\displaystyle \frac{3}{4}n=9$

$\displaystyle \frac{4}{3}\left(\frac{3}{4}\cdot n\right)=\left(\frac{4}{3}\right)\left(9 \right )$

$\displaystyle n=\frac{36}{3}=12$