Solve for y

To solve for \( y \) in the equation

\[ -42 - 11y = -97, \]

we can start by isolating the term with \( y \).

First, add 42 to both sides of the equation:

\[ -11y = -97 + 42. \]

Calculating the right side:

\[ -97 + 42 = -55, \]

so the equation now reads:

\[ -11y = -55. \]

Next, divide both sides by -11:

\[ y = \frac{-55}{-11}. \]

This simplifies to:

\[ y = 5. \]

Thus, the solution is:

\[ \boxed{5}. \]

To solve for \( a \) in the equation

\[ -7a + 28 = 7, \]

we can start by isolating the term with \( a \).

First, subtract 28 from both sides of the equation:

\[ -7a = 7 - 28. \]

Calculating the right side:

\[ 7 - 28 = -21, \]

so the equation now reads:

\[ -7a = -21. \]

Next, divide both sides by -7:

\[ a = \frac{-21}{-7}. \]

This simplifies to:

\[ a = 3. \]

Thus, the solution is:

\[ \boxed{3}. \]

To solve for \( a \) in the equation

\[ \frac{10}{3} a - 18 = 6, \]

let's start by isolating the term with \( a \).

First, add 18 to both sides of the equation:

\[ \frac{10}{3} a = 6 + 18. \]

Calculating the right side:

\[ 6 + 18 = 24, \]

so we have:

\[ \frac{10}{3} a = 24. \]

Next, to solve for \( a \), multiply both sides by the reciprocal of \( \frac{10}{3} \), which is \( \frac{3}{10} \):

\[ a = 24 \times \frac{3}{10}. \]

Calculating the right side:

\[ a = \frac{72}{10} = 7.2. \]

Thus, the solution is:

\[ \boxed{7.2}. \]

No problem! Let's solve for \( a \) in the equation

\[ \frac{3}{10} a - 18 = 6. \]

1. Add 18 to both sides to isolate the term with \( a \):

   \[ \frac{3}{10} a = 6 + 18. \]

   This simplifies to:

   \[ \frac{3}{10} a = 24. \]

2. Multiply both sides by the reciprocal of \( \frac{3}{10} \), which is \( \frac{10}{3} \):

   \[ a = 24 \times \frac{10}{3}. \]

3. Calculate the right side:

   \[ a = \frac{240}{3} = 80. \]

Thus, the solution is:

\[ \boxed{80}. \]

To solve for \( y \) in the equation

\[ 82 = 4 - \frac{6}{7} y, \]

we'll start by isolating the term with \( y \).

1. Subtract 4 from both sides:

   \[ 82 - 4 = -\frac{6}{7} y. \]

   This simplifies to:

   \[ 78 = -\frac{6}{7} y. \]

2. Multiply both sides by \(-\frac{7}{6}\) to solve for \( y \):

   \[ y = 78 \times -\frac{7}{6}. \]

3. Calculate the right side:

   \[ y = -\frac{78 \times 7}{6}. \]

   First, simplify \( \frac{78}{6} \):

   \[ \frac{78}{6} = 13, \]

   thus,

   \[ y = -13 \times 7 = -91. \]

So, the solution is:

\[ \boxed{-91}. \]