https://file.aiquickdraw.com/mathbot/file/1725459365692h9v4v1d6.jpg

Let's analyze the diagram and the questions based on the image you provided.

### 1. **Algebraic Expression for GK:**

In the diagram:
- **GH** is represented as \( x + 3 \).
- **HJ** is represented as \( y \).
- **JK** is represented as \( 5x - 1 \).

The entire segment **GK** is the sum of these three segments:

\[
\text{GK} = \text{GH} + \text{HJ} + \text{JK} = (x + 3) + y + (5x - 1)
\]

Simplifying the expression:

\[
\text{GK} = x + 5x + y + 3 - 1 = 6x + y + 2
\]

So, the algebraic expression representing **GK** is **\( 6x + y + 2 \)**.

### 2. **Finding GH and JK if GK = 44:**

Given that \( GK = 44 \):

\[
6x + y + 2 = 44
\]

Subtract 2 from both sides:

\[
6x + y = 42
\]

To find **GH** and **JK**, we need more information (like values for \( x \) and \( y \)). Since those aren't provided, you would need either \( x \) or \( y \) to find the exact lengths of GH and JK.

### 3. **Expression for GK (Simplified):**

If we are asked to simplify GK without additional steps, the expression \( 6x + y + 2 \) is already in its simplest form.

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### Do you want details or have any questions?
Here are some additional questions that expand on the topic:

1. If \( x = 5 \), what are the values of GH, HJ, and JK?
2. If \( y = 8 \), solve for \( x \) using \( 6x + y = 42 \).
3. What would GK be if \( x = 3 \) and \( y = 12 \)?
4. How would the expression change if JK were \( 4x + 7 \) instead of \( 5x - 1 \)?
5. Can you find the values of GH and JK if \( y = 6 \) and GK = 56?

**Tip:** When solving problems with algebraic expressions, always combine like terms and simplify as much as possible to avoid errors.

What algebraic expression represents GK? If GK = 44, what are GH and JK?

Learn how to express the segment GK as an algebraic expression using the given segments GH, HJ, and JK. Solve for GH and JK when GK is given as 44, suitable for students in Grades 7-9.

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