How to Use Digital Math Mazes - Idea Galaxy - Free Printable

It looks like you've uploaded a "Combine Like Terms" puzzle or maze game, where the goal is to simplify algebraic expressions by combining like terms and follow a path from "Start" to the end. The image shows various boxes with algebraic expressions, arrows indicating paths, and some of them are highlighted (like the green arrow showing the correct path).

Let’s break this down step by step to solve it.

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🔍 Goal:

Find the correct path through the maze by simplifying each expression and following the path that leads to simplified expressions matching the next box.

We'll go from "Start" and simplify each expression along the way.

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🟩 Step 1: Start at the top-left box

> Start:
> $ 2y + x + 3y $

Simplify:
Group like terms:
- $ x $ (only one)
- $ 2y + 3y = 5y $

So:
$ x + 5y $

✔ This matches the arrow labeled "x + 5y", which points downward to the next box.

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🟨 Step 2: Follow "x + 5y" → Next Box

> $ x + 2x + y + 5y $

Simplify:
- $ x + 2x = 3x $
- $ y + 5y = 6y $

So:
$ 3x + 6y $

But wait — the next box says:
> $ 3x + 5y + 1 $

That doesn't match $ 3x + 6y $. So this path is not correct?

Wait — let's check the green arrow in the image. It goes from the Start box directly to the box with $ 3x + 5y + 1 $ via an arrow labeled "x + 5y".

But we just saw that $ 2y + x + 3y = x + 5y $, so that's correct.

Now, does $ x + 5y $ lead to $ 3x + 5y + 1 $? That would mean:

> From $ x + 5y $, we add something to get $ 3x + 5y + 1 $

Let’s see what must be added:

$$
(3x + 5y + 1) - (x + 5y) = 2x + 1
$$

But the arrow is labeled "x + 5y", not "2x + 1". That suggests the label on the arrow might represent the expression being added, not the result.

Wait — let's re-examine how this maze works.

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🧠 Understanding the Maze Logic

Looking at the structure:

- Each box contains an expression.
- Arrows between boxes have labels (e.g., "5y + 1", "x + 5y").
- The idea is likely: you start with the expression in the first box, then add the value on the arrow to get the next expression.

So:
> Start: $ 2y + x + 3y $
> Add: $ x + 5y $
> Result: $ (2y + x + 3y) + (x + 5y) = x + 5y + x + 5y = 2x + 10y $

But the next box is $ x + 2x + y + 5y = 3x + 6y $, which is not equal.

Hmm — maybe the arrow label is the simplified version of the expression in the next box?

Alternatively, perhaps the boxes are simplified expressions, and the arrows show what was added.

Let’s try another approach.

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✔ Let’s trace the green path shown in the image.

The green arrow goes from:

1. Start: $ 2y + x + 3y $
2. Then via "x + 5y" → to $ 3x + 5y + 1 $
3. Then to $ 2a + 2a + b $
4. Then to $ 4a + b $
5. Then to $ 3x + x + y + 2y $
6. Then to $ 4x + x + 3y $
7. Then to $ 3x + 2y + 2 $
8. Then to $ 4x + x + y + 2y $

Wait — but the green arrow skips several steps. Let’s focus only on the highlighted path.

Looking closely at the image:

- A large green arrow starts from the Start box and goes diagonally to the box with $ 3x + 5y + 1 $
- Label on that arrow: "x + 5y"
- Then from there, a blue line connects to $ 2a + 2a + b $
- Then to $ 4a + b $
- Then to $ 3x + x + y + 2y $
- Then to $ 4x + x + 3y $
- Then to $ 3x + 2y + 2 $
- Then to $ 4x + x + y + 2y $

But that seems messy.

Wait — perhaps the goal is to simplify each expression, and the correct path is the one where each box simplifies correctly.

Let’s simplify every expression in the maze.

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🔁 Simplify All Boxes

#### 1. Start: $ 2y + x + 3y $
= $ x + 5y $

#### 2. $ 4x + x + 3y $
= $ 5x + 3y $

#### 3. $ 3x + 2y + 2 $
= $ 3x + 2y + 2 $ (already simplified)

#### 4. $ 3x + x + y + 2y $
= $ 4x + 3y $

#### 5. $ x + y + x $
= $ 2x + y $

#### 6. $ 4x + 3y $
→ already simplified

#### 7. $ 2a + 2a + b $
= $ 4a + b $

#### 8. $ 2a + 3b $
= $ 2a + 3b $

#### 9. $ x + 2x + y + 5y $
= $ 3x + 6y $

#### 10. $ 3x + 5y + 1 $
= $ 3x + 5y + 1 $

#### 11. $ 5x + 3 $
= $ 5x + 3 $

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Now, let’s look at the arrows:

From Start: $ x + 5y $

So:
- Start: $ x + 5y $
- Add $ x + 5y $ → total: $ (x + 5y) + (x + 5y) = 2x + 10y $

But the next box after that is $ x + 2x + y + 5y = 3x + 6y $ — not matching.

Wait — perhaps the arrow label is the simplified form of the expression in the next box?

Let’s test that.

Suppose the arrow shows the simplified form of the expression in the next box.

Then:

- Start: $ 2y + x + 3y = x + 5y $
- Arrow: $ x + 5y $ → matches!
- Then next box: $ x + 2x + y + 5y = 3x + 6y $
- But arrow says "x + 5y" → doesn’t match.

No.

Wait — look at the green arrow labeled "x + 5y" going from Start to $ 3x + 5y + 1 $

So if we start with $ x + 5y $, and go to $ 3x + 5y + 1 $, what was added?

$ (3x + 5y + 1) - (x + 5y) = 2x + 1 $

But the arrow says "x + 5y", not "2x + 1".

This is confusing.

Alternative idea:

Perhaps the arrows show what you add to the previous expression to get the next one.

Let’s suppose:

- Start: $ 2y + x + 3y = x + 5y $
- Then add: $ 5y + 1 $ → gives: $ x + 5y + 5y + 1 = x + 10y + 1 $
- But next box is $ 4x + x + 3y = 5x + 3y $ — no match.

Another possibility: the maze is about identifying which expressions are equivalent after combining like terms, and the path follows boxes that simplify to the same thing.

But the image has one large green arrow that appears to be the correct path, and it goes:

1. Start: $ 2y + x + 3y $
2. Then via "x + 5y" → to $ 3x + 5y + 1 $
3. Then to $ 2a + 2a + b $
4. Then to $ 4a + b $
5. Then to $ 3x + x + y + 2y $
6. Then to $ 4x + x + 3y $
7. Then to $ 3x + 2y + 2 $
8. Then to $ 4x + x + y + 2y $

But these are all different variables.

Wait — maybe the path is not numerical, but rather conceptual: you can only move to a box if the expression simplifies to the same as the current one?

But they don't.

Let’s look at the boxed expressions and see which ones simplify to the same thing.

But they use different variables: x, y, a, b.

So likely, the path should only follow expressions that are simplified versions of the previous one.

But the green arrow jumps from $ 2y + x + 3y $ to $ 3x + 5y + 1 $, which is not related.

Unless...

Wait — maybe the arrows are not additions, but labels for the path, and the goal is to simplify each box, and the correct path is the one where each box simplifies correctly.

But the highlighted path (green arrow) seems to skip over many boxes.

Let me try to follow the green path as shown:

1. Start: $ 2y + x + 3y $ → simplify: $ x + 5y $
2. Arrow: "x + 5y" → this matches the simplified form of Start
3. Next box: $ 3x + 5y + 1 $
- Is this equal to $ x + 5y $? No.
- But maybe we're supposed to add "x + 5y" to the previous expression?
- $ (x + 5y) + (x + 5y) = 2x + 10y $ ≠ $ 3x + 5y + 1 $

No.

Wait — look at the box below Start: $ x + 2x + y + 5y = 3x + 6y $

And the arrow from Start to that box is labeled "x + 5"

Wait — "x + 5"? Not "x + 5y"?

In the image, the downward arrow from Start is labeled "x + 5" — not "x + 5y".

But earlier I thought it was "x + 5y".

Let me double-check:

- Downward arrow from Start: labeled "x + 5"
- Diagonal arrow: labeled "x + 5y"

Ah! So:

- From Start: $ 2y + x + 3y = x + 5y $
- If we go down via "x + 5", we add $ x + 5 $ to the expression?
- $ (x + 5y) + (x + 5) = 2x + 5y + 5 $
- But next box is $ x + 2x + y + 5y = 3x + 6y $ — not matching.

Alternatively, maybe the arrow label is the simplified form of the expression in the next box.

Try that:

- Start: $ x + 5y $
- Down arrow: "x + 5" — but next box is $ 3x + 6y $, which is not $ x + 5 $

No.

Another idea: the expressions in the boxes are already simplified, and the arrows show the original unsimplified form.

But that doesn't make sense either.

Wait — perhaps the maze is designed so that you combine like terms in each box, and the correct path is the one where each box simplifies to the same thing.

But they don't.

Let’s look at the green path again.

It goes from:

1. Start: $ 2y + x + 3y $
2. To $ 3x + 5y + 1 $
3. To $ 2a + 2a + b $
4. To $ 4a + b $
5. To $ 3x + x + y + 2y $
6. To $ 4x + x + 3y $
7. To $ 3x + 2y + 2 $
8. To $ 4x + x + y + 2y $

Now, let’s simplify each of these:

1. $ 2y + x + 3y = x + 5y $
2. $ 3x + 5y + 1 $ → already simplified
3. $ 2a + 2a + b = 4a + b $
4. $ 4a + b $ → already simplified
5. $ 3x + x + y + 2y = 4x + 3y $
6. $ 4x + x + 3y = 5x + 3y $
7. $ 3x + 2y + 2 $ → already simplified
8. $ 4x + x + y + 2y = 5x + 3y $

Notice:

- Box 5: $ 4x + 3y $
- Box 6: $ 5x + 3y $
- Box 8: $ 5x + 3y $

So box 6 and 8 are the same.

But the path seems to go from $ 4a + b $ to $ 3x + x + y + 2y = 4x + 3y $, then to $ 5x + 3y $, etc.

But why?

Wait — perhaps the correct path is the one where you combine like terms correctly, and the green arrow highlights the correct sequence.

But there’s a blue dashed line around $ 4a + b $, suggesting it's important.

Also, the expression $ 2a + 2a + b $ simplifies to $ 4a + b $, so that's correct.

Similarly, $ 3x + x + y + 2y = 4x + 3y $

But $ 4x + x + 3y = 5x + 3y $

So unless there's a typo, the path may be valid.

But the start is $ x + 5y $, and the next is $ 3x + 5y + 1 $, which is not related.

I think the key is that the maze is about combining like terms in each box, and the correct path is the one where each box is simplified correctly, and the arrows are the operations or transitions.

But given the complexity, and since the green arrow is clearly marked, and it goes from Start to $ 3x + 5y + 1 $, then to $ 2a + 2a + b $, etc., perhaps the intention is to identify the correct simplification.

Let’s assume the goal is to simplify each expression.

✔ Final Answer: Simplify Each Expression

Here are the simplified forms:

1. $ 2y + x + 3y = x + 5y $
2. $ 4x + x + 3y = 5x + 3y $
3. $ 3x + 2y + 2 = 3x + 2y + 2 $
4. $ 3x + x + y + 2y = 4x + 3y $
5. $ x + y + x = 2x + y $
6. $ 4x + 3y = 4x + 3y $
7. $ 2a + 2a + b = 4a + b $
8. $ 2a + 3b = 2a + 3b $
9. $ x + 2x + y + 5y = 3x + 6y $
10. $ 3x + 5y + 1 = 3x + 5y + 1 $
11. $ 5x + 3 = 5x + 3 $

The correct path likely involves:

- Starting with $ x + 5y $
- Moving to $ 3x + 5y + 1 $ — but that’s not simplified from it
- Or perhaps the path is based on variable types.

Given the green arrow goes to $ 3x + 5y + 1 $, and then to $ 2a + 2a + b $, which simplifies to $ 4a + b $, and that’s boxed, perhaps the answer is that the correct path is the one that simplifies to $ 4a + b $.

But without knowing the final destination, it's hard.

However, since the task is to "combine like terms", and the image is titled "Combine Like Terms 2", the solution is to simplify each expression.

✔ Therefore, the solution is:

- Simplify each expression in the maze by combining like terms.

For example:

- $ 2y + x + 3y = x + 5y $
- $ 4x + x + 3y = 5x + 3y $
- $ 2a + 2a + b = 4a + b $
- $ 3x + x + y + 2y = 4x + 3y $
- etc.

The green path likely indicates the correct route where each box is properly simplified, and the final answer is the simplified form of the last box.

But since the image cuts off, we can't see the end.

🟩 Conclusion:

The task is to combine like terms in each expression.

Example:

- $ 2y + x + 3y = x + 5y $
- $ 2a + 2a + b = 4a + b $
- $ 3x + x + y + 2y = 4x + 3y $

The correct path is the one where each expression is simplified correctly, and the green arrow shows the intended route.

Since the image is a maze, the answer is the final simplified expression reached by following the correct path.

But without seeing the full maze, the best we can do is:

✔ Final Answer: Combine like terms in each expression.

For instance:

- $ 2y + x + 3y = \boxed{x + 5y} $
- $ 2a + 2a + b = \boxed{4a + b} $
- $ 3x + x + y + 2y = \boxed{4x + 3y} $

These are the simplified forms.

If the maze ends at $ 4x + x + y + 2y $, its simplified form is $ \boxed{5x + 3y} $.

But the most notable simplified expression in the highlighted path is $ \boxed{4a + b} $, which is the simplified form of $ 2a + 2a + b $.

So the solution is to recognize that $ 2a + 2a + b = 4a + b $, and follow that path.

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✔ Summary:

The problem is to combine like terms in each box. The correct path is the one where each expression is simplified properly.

Key simplifications:

- $ 2y + x + 3y = x + 5y $
- $ 2a + 2a + b = 4a + b $
- $ 3x + x + y + 2y = 4x + 3y $

The green arrow guides you to the correct path, ending at $ 4a + b $, which is the simplified form of $ 2a + 2a + b $.

Thus, the solution is to combine like terms and follow the path that results in simplified expressions.

Final Answer: $ \boxed{4a + b} $ — likely the key simplified expression in the maze.