In the equation, $m$ is being divided by $8.$ To isolate $m$, we can perform the opposite operation, which is multiplying by $8.$ So, we multiply both sides of the equation by $8.$

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac m 8&= 11 \\[5pt] 8 \cdot \dfrac m 8 &= 8 \cdot 11 \\[5pt] \dfrac{8m}{8} &= 88 } \end{eqnarray}

Now, we can cancel a common factor of $8$ from both the numerator and denominator.

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac{8m}{8} &= 88 \\[5pt] \dfrac{\cancel{8}m}{\cancel{8}} &= 88 \\[5pt] m&=88 } \end{eqnarray}

In the equation, $z$ is being divided by $6.$ To isolate $z$, we can perform the opposite operation, which is multiplying by $6.$ So, we multiply both sides of the equation by $6.$

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac{z}{6}&=-6 \\[5pt] 6 \cdot \dfrac{z}{6}&=6 \cdot(-6) \\[5pt] \dfrac{6z}{6} &= -36 } \end{eqnarray}

Now, we can cancel a common factor of $6$ from both the numerator and denominator.

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac{6z}{6} &= -36 \\[5pt] \dfrac{\cancel{6}z}{\cancel{6}} &= -36 \\[5pt] z&=-36 } \end{eqnarray}

First, let's swap the left and right-hand sides so that the variable is on the left-hand side.

\[ \dfrac{g}{12}=\dfrac{1}{4} \]

In this equation, $g$ is being divided by $12.$ To isolate $g$, we can perform the opposite operation, which is multiplying by $12.$ So, we multiply both sides of the equation by $12$ and simplify.

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac{g}{12}&=\dfrac{1}{4} \\[5pt] 12 \cdot \dfrac{g}{12}&=12 \cdot\left(\dfrac{1}{4}\right) \\[5pt] \dfrac{12g}{12} &= \dfrac{12}{4} \\[5pt] \dfrac{12g}{12} &= 3 \\[5pt] \dfrac{\cancel{12}g}{\cancel{12}} &=3 \\[5pt] g&=3 } \end{eqnarray}

First, let's swap the left and right-hand sides so that the variable is on the left-hand side.

\[ \dfrac{m}{6}=-\dfrac{1}{3} \]

In this equation, $m$ is being divided by $6.$ To isolate $m$, we can perform the opposite operation, which is multiplying by $6.$ So, we multiply both sides of the equation by $6$ and simplify.

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac{m}{6}&=-\dfrac{1}{3} \\[5pt] 6 \cdot \dfrac{m}{6}&=6 \cdot\left(-\dfrac{1}{3}\right) \\[5pt] \dfrac{6m}{6} &= -\dfrac{6}{3} \\[5pt] \dfrac{6m}{6} &= -2 \\[5pt] \dfrac{\cancel{6}m}{\cancel{6}} &=-2 \\[5pt] m&=-2 } \end{eqnarray}

First, let's remove the negative sign from the variable. To do this, we multiply both sides of the equation by $-1.$

\begin{align*} -\dfrac{c}{5}&=3 \\[5pt] (-1) \cdot \left( -\dfrac{c}{5} \right) &=(-1) \cdot 3 \\[5pt] \dfrac{c}{5}&=-3 \end{align*}

In the equation above, $c$ is being divided by $5.$ To isolate $c$, we can perform the opposite operation, which is multiplying by $5.$ So, we multiply both sides of the equation by $5$ and simplify.

\[ \require{cancel} \eqalign{ \dfrac{c}{5}&=-3 \\[5pt] 5 \cdot \dfrac{c}{5} &=5 \cdot \left( -3 \right) \\[5pt] \dfrac{5c}{5} &= -15 \\[5pt] \dfrac{\cancel{5}c}{\cancel{5}} &= -15 \\[5pt] c &= -15 } \]

First, let's remove the negative sign from the variable. To do this, we multiply both sides of the equation by $-1.$

\begin{align*} -\dfrac{p}{3}&=\dfrac{1}{6} \\[5pt] (-1) \cdot \left( -\dfrac{p}{3} \right) &=(-1) \cdot \dfrac{1}{6} \\[5pt] \dfrac{p}{3}&=-\dfrac{1}{6} \end{align*}

In the equation above, $p$ is being divided by $3.$ To isolate $p$, we can perform the opposite operation, which is multiplying by $3.$ So, we multiply both sides of the equation by $3$ and simplify.

\[ \require{cancel} \eqalign{ \dfrac{p}{3}&=-\dfrac{1}{6} \\[5pt] 3 \cdot \dfrac{p}{3} &=3 \cdot \left( -\dfrac{1}{6} \right) \\[5pt] \dfrac{3p}{3} &= -\dfrac{3}{6} \\[5pt] \dfrac{\cancel{3}p}{\cancel{3}} &= -\dfrac{3}{6} \\[5pt] p &= -\dfrac{1}{2} } \]

The variable $y$ is being multiplied by $6.$ To isolate $y$, we can perform the opposite operation, which is dividing by $6.$ So, we divide both sides of the equation by $6.$

\begin{eqnarray} \require{cancel} \eqalign{ 6y &= 14 \\[5pt] \dfrac {6y} 6 &= \dfrac {14} 6 \\[5pt] \dfrac {6y} 6 &= \dfrac {7} 3 } \end{eqnarray}

Now, we can cancel a common factor of $6$ from both the numerator and denominator.

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac {6y} 6 &= \dfrac {7} 3 \\[5pt] \dfrac {\cancel{6}y}{\cancel{6}} &= \dfrac {7} 3 \\[5pt] y &= \dfrac 7 3 } \end{eqnarray}

The variable $x$ is being multiplied by $-4.$ To isolate $x$, we can perform the opposite operation, which is dividing by $-4.$ So, we divide both sides of the equation by $-4.$

\[ \require{cancel} \eqalign{ -4x &=-36 \\[5pt] \dfrac {-4x} {-4} &= \dfrac {-36} {-4} \\[5pt] \dfrac {-4x} {-4} &= 9 } \]

Now, we can cancel a common factor of $-4$ from both the numerator and denominator.

\begin{eqnarray} \require{cancel} \eqalign{ \dfrac {-4x} {-4} &= 9 \\[5pt] \dfrac {\cancel{-4}x} {\cancel{-4}} &= 9\\[5pt] x &=9 } \end{eqnarray}