https://file.aiquickdraw.com/mathbot/file/17284344414362hhf4wr5.jpg

The equation in the image is:

\[
\frac{4}{11}z + 4 = 32
\]

Let's solve it step by step.

### Step 1: Subtract 4 from both sides
\[
\frac{4}{11}z + 4 - 4 = 32 - 4
\]
This simplifies to:
\[
\frac{4}{11}z = 28
\]

### Step 2: Multiply both sides by 11 to eliminate the denominator
\[
4z = 28 \times 11
\]
\[
4z = 308
\]

### Step 3: Divide both sides by 4
\[
z = \frac{308}{4}
\]
\[
z = 77
\]

### Final Answer:
\[
z = 77
\]

Would you like more details on any step or have any other questions?

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Here are 5 related questions to expand on this:

1. What happens if the constant on the right side is negative instead of positive?
2. How would you solve if the coefficient of \( z \) was a fraction like \(\frac{4}{11} \)?
3. What are the properties of equations with fractions, and how can we simplify them?
4. Can we solve similar equations with more complex terms, like involving exponents or square roots?
5. How can you check if the solution you obtained is correct?

**Tip**: When dealing with fractions in equations, try to eliminate them by multiplying both sides by the denominator early on to simplify the process.

This page provides a detailed step-by-step solution for the linear equation 4/11 * z + 4 = 32, covering essential algebraic concepts such as solving for a variable with fractions. Suitable for students in Grades 6-8.

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