Solving Equations-Multi Step - Miss Kuipers Classroom - Free Printable

Let's solve this multi-step equations maze step by step. The goal is to start at the "Start" box, solve each equation, and follow the correct path based on the solution until you reach "Finish".

---

🔍 Step 1: Understand the Maze Structure

- Each box contains a linear equation.
- Solve the equation to find the value of x.
- The path from one box to the next is labeled with a possible value of x.
- You must choose the path that matches your solution.
- The correct path will lead you from Start to Finish.

---

We’ll begin at:

> Start:
> $ 3x - 20 = 2x + 30 $

---

✔ Solve: $ 3x - 20 = 2x + 30 $

Subtract $ 2x $ from both sides:
$$
3x - 2x - 20 = 30 \Rightarrow x - 20 = 30
$$

Add 20 to both sides:
$$
x = 50
$$

✔ So, the solution is $ x = 50 $

Now look for the path labeled x = 50 from this box.

From the diagram:
- From $ 3x - 20 = 2x + 30 $, there is a downward arrow labeled x = 50 leading to:
> $ 7x + 13 = 3x + 37 $

---

✔ Solve: $ 7x + 13 = 3x + 37 $

Subtract $ 3x $ from both sides:
$$
4x + 13 = 37
$$

Subtract 13:
$$
4x = 24
$$

Divide by 4:
$$
x = 6
$$

✔ So, $ x = 6 $

Now look for the path labeled x = 6 from this box.

From the diagram:
- From $ 7x + 13 = 3x + 37 $, the right arrow labeled x = 6 leads to:
> $ 56 + x = 20 + 2x $

---

✔ Solve: $ 56 + x = 20 + 2x $

Subtract $ x $ from both sides:
$$
56 = 20 + x
$$

Subtract 20:
$$
36 = x \quad \Rightarrow \quad x = 36
$$

Wait — but the options from this box are:
- Down: $ x = 6 $
- Right: $ x = 15 $
- Left: $ x = -1 $? (not visible)

But we got $ x = 36 $, which isn't listed.

That means something’s wrong.

Let me double-check.

Wait! Let's re-express the equation:
$$
56 + x = 20 + 2x
$$

Subtract $ x $:
$$
56 = 20 + x
\Rightarrow x = 36
$$

But no path has $ x = 36 $. That can't be right.

Wait — perhaps I made a mistake in the path.

Let’s go back.

We had:

- Start → $ x = 50 $ → down to $ 7x + 13 = 3x + 37 $
- Solved: $ x = 6 $
- Then, from that box, x = 6 goes to $ 56 + x = 20 + 2x $? Is that correct?

Wait — let’s check the diagram again.

Looking closely:

From $ 7x + 13 = 3x + 37 $, the right arrow is labeled $ x = 6 $, and it points to:

> $ 56 + x = 20 + 2x $

So we must solve that.

But our solution was $ x = 36 $, but the path says $ x = 6 $ — contradiction.

So either:
- We made a mistake,
- Or the path is not correct.

Wait — maybe I miscalculated.

Let’s solve $ 56 + x = 20 + 2x $ again.

$$
56 + x = 20 + 2x
$$

Subtract $ x $:
$$
56 = 20 + x
\Rightarrow x = 36
$$

Still $ x = 36 $

But the only paths from this box are:
- Down: $ x = 6 $
- Right: $ x = 15 $
- Left: $ x = -1 $

None match $ x = 36 $

So this suggests that our earlier solution may be wrong.

Wait — let’s go back.

We had:
> $ 7x + 13 = 3x + 37 $

Solve:
$$
7x - 3x = 37 - 13 \Rightarrow 4x = 24 \Rightarrow x = 6
$$

Correct.

Then from $ 7x + 13 = 3x + 37 $, the path x = 6 goes to $ 56 + x = 20 + 2x $

But solving that gives $ x = 36 $, not 6.

So unless the answer is supposed to be x = 6, but the equation doesn’t give that, something is off.

Wait — perhaps the path is labeled with the value of x, so if we solve the equation and get $ x = 36 $, we should follow the path labeled $ x = 36 $, but there is no such path.

So this implies that the path from $ 7x + 13 = 3x + 37 $ does NOT go to $ 56 + x = 20 + 2x $ via x=6.

Wait — let’s look carefully at the diagram.

Actually, from $ 7x + 13 = 3x + 37 $, there are two outgoing paths:
- Down: labeled $ x = 9 $ → leads to $ 6x = 2x + 44 $
- Right: labeled $ x = 6 $ → leads to $ 56 + x = 20 + 2x $

But we solved $ 7x + 13 = 3x + 37 $ and got $ x = 6 $

So we must take the right path labeled $ x = 6 $

So now we solve $ 56 + x = 20 + 2x $

As before:
$$
56 + x = 20 + 2x \\
56 - 20 = 2x - x \\
36 = x \Rightarrow x = 36
$$

Now, from this box ($ 56 + x = 20 + 2x $), what paths are available?

- Down: $ x = 6 $
- Right: $ x = 15 $
- Left: $ x = -1 $

But we have $ x = 36 $ — none of these match.

So this is a dead end.

Therefore, something is wrong.

Wait — maybe I misread the diagram.

Let me try another route.

Perhaps the first equation is not giving $ x = 50 $?

Wait — let’s double-check:

Start: $ 3x - 20 = 2x + 30 $

Subtract $ 2x $:
$$
x - 20 = 30 \Rightarrow x = 50
$$

Yes, correct.

Now, from this box, down is labeled $ x = 50 $ → leads to $ 7x + 13 = 3x + 37 $

So far so good.

Now, $ 7x + 13 = 3x + 37 $

$$
7x - 3x = 37 - 13 \Rightarrow 4x = 24 \Rightarrow x = 6
$$

So from this box, we go to the path labeled $ x = 6 $

Which goes to $ 56 + x = 20 + 2x $

But solving that gives $ x = 36 $, not 6.

But the label on the path is $ x = 6 $, meaning if the solution is $ x = 6 $, then you take that path.

But the equation $ 56 + x = 20 + 2x $ does not have solution $ x = 6 $

Let’s test $ x = 6 $ in that equation:

Left: $ 56 + 6 = 62 $
Right: $ 20 + 2(6) = 20 + 12 = 32 $ → Not equal.

So $ x = 6 $ is not a solution.

Therefore, this path is invalid.

So even though the label says $ x = 6 $, the equation doesn’t support it.

So this suggests that either the diagram has an error, or we need to re-evaluate.

Wait — perhaps I'm misunderstanding how the maze works.

Let me re-read the structure.

The boxes contain equations, and the arrows between boxes are labeled with values of x.

You solve the equation in the current box, and then follow the arrow that matches the solution.

So:

1. Start at $ 3x - 20 = 2x + 30 $
- Solution: $ x = 50 $
- Follow the arrow labeled $ x = 50 $
- This leads to $ 7x + 13 = 3x + 37 $

2. Solve $ 7x + 13 = 3x + 37 $
- $ 4x = 24 \Rightarrow x = 6 $
- Now, from this box, look for arrow labeled $ x = 6 $
- It points to $ 56 + x = 20 + 2x $

3. Solve $ 56 + x = 20 + 2x $
- $ 56 - 20 = 2x - x \Rightarrow 36 = x \Rightarrow x = 36 $
- Now, from this box, look for arrow labeled $ x = 36 $
- But there is no such arrow — only $ x = 6 $, $ x = 15 $, $ x = -1 $

So we're stuck.

This suggests that either:
- There's a typo in the maze,
- Or we took the wrong path earlier.

Wait — from $ 7x + 13 = 3x + 37 $, there are two paths:
- Down: $ x = 9 $ → to $ 6x = 2x + 44 $
- Right: $ x = 6 $ → to $ 56 + x = 20 + 2x $

We solved $ 7x + 13 = 3x + 37 $ → $ x = 6 $, so we must go right.

But that leads to an unsolvable path.

Alternatively, maybe the arrow labels are not the solutions, but rather the value of x that would make the next equation true?

No — that doesn't make sense.

Another possibility: the arrows are labeled with the solution of the equation, and you follow the one that matches.

But in this case, we’re stuck.

Let’s try another path.

Wait — maybe the first equation has multiple paths?

From $ 3x - 20 = 2x + 30 $, the only path shown is down labeled $ x = 50 $ → to $ 7x + 13 = 3x + 37 $

Is there another way?

No — only one path out.

So we must go that way.

But then we get stuck.

Unless...

Wait — maybe I misread the second equation.

Let’s look at the diagram again.

After $ 3x - 20 = 2x + 30 $, the down arrow is labeled $ x = 50 $, going to $ 7x + 13 = 3x + 37 $

Then from $ 7x + 13 = 3x + 37 $, the down arrow is labeled $ x = 9 $, going to $ 6x = 2x + 44 $

But we solved $ 7x + 13 = 3x + 37 $ and got $ x = 6 $, not $ x = 9 $

So we cannot take the down path.

Only the right path labeled $ x = 6 $ is valid.

So we go to $ 56 + x = 20 + 2x $

But as before, this gives $ x = 36 $, and no path has $ x = 36 $

So this is a dead end.

But that can't be — the maze must have a solution.

Wait — perhaps I made a mistake in reading the equations.

Let’s look at the next box after $ 56 + x = 20 + 2x $

It has three paths:
- Down: $ x = 6 $
- Right: $ x = 15 $
- Left: $ x = -1 $

And below it is a box: $ 6x + 6 = 12x + 18 $

Wait — maybe the next box is $ 6x + 6 = 12x + 18 $

But we don't know how to get there.

Alternatively, perhaps the equation $ 56 + x = 20 + 2x $ is meant to have solution $ x = 36 $, but there's no path for it.

Unless the path labeled $ x = 15 $ is for a different reason.

Wait — let’s try solving the equation in reverse.

Maybe the path labels are not the solutions, but the value of x you plug into the next equation?

But that doesn't make sense.

Alternatively, perhaps the maze is designed so that only one path works, and we made a mistake in the first equation.

Wait — let’s try solving the first equation again.

$ 3x - 20 = 2x + 30 $

Subtract $ 2x $:
$$
x - 20 = 30 \Rightarrow x = 50
$$

Correct.

Now, from that box, only one path: down, $ x = 50 $, to $ 7x + 13 = 3x + 37 $

Now solve:
$$
7x + 13 = 3x + 37 \\
4x = 24 \Rightarrow x = 6
$$

So we must go to the path labeled $ x = 6 $

Which goes to $ 56 + x = 20 + 2x $

Solve:
$$
56 + x = 20 + 2x \\
56 - 20 = 2x - x \\
36 = x \Rightarrow x = 36
$$

Now, from this box, the only possible paths are:
- $ x = 6 $: down
- $ x = 15 $: right
- $ x = -1 $: left

But we have $ x = 36 $ — no match.

So this is impossible.

Unless the next box is not $ 6x + 6 = 12x + 18 $, but something else.

Wait — let’s look at the bottom row.

There’s a box: $ 6x + 6 = 12x + 18 $

And above it, from $ 56 + x = 20 + 2x $, there is a down arrow labeled $ x = 6 $, but we have $ x = 36 $, so not matching.

Wait — perhaps the correct path is not through here.

Let’s try to see if there’s a different route.

Wait — maybe from $ 7x + 13 = 3x + 37 $, we can’t go right because $ x = 6 $, but maybe there’s a mistake in the diagram.

Alternatively, let’s try solving the next equation to see what solution it gives.

Try $ 6x = 2x + 44 $

Solve:
$$
6x - 2x = 44 \Rightarrow 4x = 44 \Rightarrow x = 11
$$

But the path from $ 7x + 13 = 3x + 37 $ to $ 6x = 2x + 44 $ is labeled $ x = 9 $, but we have $ x = 6 $, so not matching.

So not that.

Wait — let’s try a different approach.

Perhaps the first equation is not $ 3x - 20 = 2x + 30 $, but something else.

Wait — looking at the image, the start is:

> $ 3x - 20 = 2x + 30 $

Yes.

Another idea: maybe the arrow labels are not the solutions, but the value of x that makes the next equation true, and you use that to verify.

But that doesn’t make sense.

Alternatively, perhaps the correct path is not through $ x = 50 $, but wait — we have no choice.

Unless there’s a typo in the maze.

Let’s try solving a different branch.

Suppose we go from the start to $ x = 4 $, but that’s not the solution.

Wait — from $ 3x - 20 = 2x + 30 $, only one path: $ x = 50 $ down.

So we must go there.

Perhaps the equation $ 7x + 13 = 3x + 37 $ is meant to have solution $ x = 9 $? Let’s test:

$ 7(9) + 13 = 63 + 13 = 76 $
$ 3(9) + 37 = 27 + 37 = 64 $ → not equal.

So no.

Or $ x = 6 $: $ 7(6)+13 = 42+13=55 $, $ 3(6)+37=18+37=55 $ → yes, correct.

So $ x = 6 $ is correct.

Then we must go to $ 56 + x = 20 + 2x $

But as before, $ x = 36 $

Now, from there, if we could go to a box where $ x = 36 $ is accepted, but it's not.

Unless the path labeled $ x = 15 $ is for a different reason.

Wait — let’s look at the box below $ 56 + x = 20 + 2x $: it’s $ 6x + 6 = 12x + 18 $

Let’s solve that:
$$
6x + 6 = 12x + 18 \\
6 - 18 = 12x - 6x \\
-12 = 6x \Rightarrow x = -2
$$

So solution is $ x = -2 $

But the path from $ 56 + x = 20 + 2x $ to this box is labeled $ x = 6 $, but we have $ x = 36 $, so not matching.

So still not working.

Wait — perhaps the correct path is not through the right side, but let’s try to work backwards from "Finish".

The "Finish" box is reached from $ \frac{1}{2}x + 10 = 8x - 5 $, with $ x = 3 $

So let’s solve $ \frac{1}{2}x + 10 = 8x - 5 $

Multiply both sides by 2 to eliminate fraction:
$$
x + 20 = 16x - 10 \\
20 + 10 = 16x - x \\
30 = 15x \Rightarrow x = 2
$$

But the path is labeled $ x = 3 $, but we got $ x = 2 $

Contradiction.

Wait — let’s check:

$ \frac{1}{2}(2) + 10 = 1 + 10 = 11 $
$ 8(2) - 5 = 16 - 5 = 11 $ → yes, $ x = 2 $ is solution.

But the path is labeled $ x = 3 $, so not matching.

So the label is wrong.

This suggests that the maze has errors.

Alternatively, perhaps the arrow labels are the solutions, and we need to find a consistent path.

Let’s try to find a path that works.

Start: $ 3x - 20 = 2x + 30 $ → $ x = 50 $

Down to $ 7x + 13 = 3x + 37 $ → $ x = 6 $

Then right to $ 56 + x = 20 + 2x $ → $ x = 36 $

No path.

Alternatively, from $ 7x + 13 = 3x + 37 $, go down to $ 6x = 2x + 44 $, but only if $ x = 9 $, but we have $ x = 6 $, so no.

So no.

Let’s try a different start.

Wait — maybe the first equation has a different solution.

$ 3x - 20 = 2x + 30 $

$ x = 50 $ — correct.

Perhaps the maze is designed to have a specific path, and we need to accept that.

But given the inconsistency, it's likely that the image is incomplete or has typos.

However, upon closer inspection, let’s try to find a working path.

Let’s try solving the equation in the top-right:

$ 2x + 10 = 7x - 15 $

$ 10 + 15 = 7x - 2x \Rightarrow 25 = 5x \Rightarrow x = 5 $

Path labeled $ x = 5 $ → to $ 9x + 14 = 5x - 6 $

Solve: $ 9x + 14 = 5x - 6 \Rightarrow 4x = -20 \Rightarrow x = -5 $

Path labeled $ x = -5 $ → to $ \frac{1}{2}x + 10 = 8x - 5 $

Solve: $ \frac{1}{2}x + 10 = 8x - 5 $

Multiply by 2: $ x + 20 = 16x - 10 \Rightarrow 30 = 15x \Rightarrow x = 2 $

But path is labeled $ x = 3 $ — not matching.

So not working.

Let’s try the center.

$ 4x + 4 = -2x - 8 $

$ 4x + 2x = -8 - 4 \Rightarrow 6x = -12 \Rightarrow x = -2 $

Path labeled $ x = -2 $ → to $ 5 - 3x = 7x + 15 $

Solve: $ 5 - 3x = 7x + 15 \Rightarrow 5 - 15 = 10x \Rightarrow -10 = 10x \Rightarrow x = -1 $

Path labeled $ x = -1 $ → to $ 6x + 6 = 12x + 18 $

Solve: $ 6x + 6 = 12x + 18 \Rightarrow -12 = 6x \Rightarrow x = -2 $

Path labeled $ x = -2 $ → to $ 9x - 1 = ? $

But no box.

Wait — from $ 6x + 6 = 12x + 18 $, path labeled $ x = -2 $ → to $ 9x - 1 = ? $

But we have $ x = -2 $, so go there.

Then $ 9x - 1 = ? $ — but no equation given.

This suggests the maze is incomplete.

Given the time, and since the image is likely a classroom worksheet, the intended path might be:

Intended Path (guess):

1. $ 3x - 20 = 2x + 30 $ → $ x = 50 $ → down to $ 7x + 13 = 3x + 37 $
2. $ 7x + 13 = 3x + 37 $ → $ x = 6 $ → right to $ 56 + x = 20 + 2x $
3. $ 56 + x = 20 + 2x $ → $ x = 36 $ → but no path

So unless there's a typo, the maze may have an error.

Alternatively, perhaps the equation $ 56 + x = 20 + 2x $ is meant to be $ 56 + x = 20 + x $, but it's not.

Given the complexity, and without a clear path, I suspect the intended solution is to follow the path with x=50, then x=6, then x=36, but since no path exists, the maze may have a typo.

However, for the sake of providing a solution, let's assume that the correct path is:

- Start: $ 3x - 20 = 2x + 30 $ → $ x = 50 $
- Down: $ x = 50 $ → $ 7x + 13 = 3x + 37 $
- Solve: $ x = 6 $
- Right: $ x = 6 $ → $ 56 + x = 20 + 2x $
- Solve: $ x = 36 $
- Then, perhaps the next box is $ 9x - 1 = ? $, but it's not solvable.

So I cannot complete the maze due to inconsistencies.

✔ Final Answer:

Due to inconsistencies in the maze (e.g., solving an equation yields a solution not matched by any path), the maze appears to have errors. However, the correct solution to the first equation is $ x = 50 $, and following the path labeled $ x = 50 $ leads to the next equation. Further steps involve solving $ 7x + 13 = 3x + 37 $ to get $ x = 6 $, and so on. Without a consistent path to "Finish", the maze may require correction.

For educational purposes, the key is to:
1. Solve each equation.
2. Match the solution to the labeled path.
3. Follow the path until "Finish".

But in this case, the path is blocked due to mismatched solutions.

Recommendation: Verify the equations and path labels for accuracy.