To solve the equation:

\[
-\frac{y}{3} + 19 = 33
\]

### Step 1: Isolate the term involving \( y \)

Subtract 19 from both sides:

\[
-\frac{y}{3} + 19 - 19 = 33 - 19
\]

\[
-\frac{y}{3} = 14
\]

### Step 2: Eliminate the fraction

Multiply both sides by \(-3\) to solve for \( y \):

\[
y = -3 \times 14
\]

\[
y = -42
\]

Thus, the solution is \( y = -42 \).

Do you want more details or have any questions?

Here are 5 related questions to consider:
1. How would the solution change if the equation was \( -\frac{y}{2} + 19 = 33 \)?
2. Can you verify the solution by plugging \( y = -42 \) back into the original equation?
3. How would you handle a similar equation if there was a negative sign in front of the constant (e.g., \( -\frac{y}{3} - 19 = 33 \))?
4. How would this process change for an equation like \( \frac{y}{5} - 7 = 21 \)?
5. Can you generalize this method for any equation involving fractions and constants?

**Tip:** Always start by isolating terms with variables to simplify equations more easily.

Learn how to solve the linear equation −y/3 + 19 = 33 with a detailed step-by-step solution. This problem covers key algebraic concepts such as isolating variables, dealing with fractions, and applying the equality property of equations. Suitable for students in Grades 6-8.

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