Differentiated math activity where students solve linear equations to cross off answers on a grid.

It looks like you've uploaded an image of a math worksheet titled "Answer GRID", which contains a 3×4 grid of linear equations. The instructions say: *"Cross off each answer, then total..."* — but the full instruction is cut off.

However, based on the layout and typical structure of such worksheets, this appears to be a "cross off" or "elimination" activity where students solve each equation, find the value of $ x $, and then cross off that answer from a list (not shown here), possibly to reveal a pattern, word, or final sum.

But since the answer choices or values to cross off are not visible, we can't complete the "cross off" part without more information.

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Step 1: Solve Each Equation

Let’s go through each equation in the grid and solve for $ x $. We'll organize them by color rows:

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#### 🔴 RED Row

1. $ 17 = 6x + 5 $
$ 17 - 5 = 6x $ → $ 12 = 6x $ → $ x = 2 $

2. $ 3x + 12 = 24 $
$ 3x = 12 $ → $ x = 4 $

3. $ 14 = 4x - 10 $
$ 14 + 10 = 4x $ → $ 24 = 4x $ → $ x = 6 $

4. $ 4x + 7 = ? $ ← Incomplete!
This one is missing the right-hand side. It says $ 4x + 7 = $, but nothing follows. Likely a typo or missing number. We’ll skip it for now.

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#### 🟡 AMBER Row

5. $ 4x - 5 = 5 $
$ 4x = 10 $ → $ x = 2.5 $ or $ \frac{5}{2} $

6. $ 36 = 6x - 24 $
$ 36 + 24 = 6x $ → $ 60 = 6x $ → $ x = 10 $

7. $ 8x + 6 = 10 $
$ 8x = 4 $ → $ x = 0.5 $ or $ \frac{1}{2} $

8. $ 19 = 2x + 7 $? Wait — actually, it says: $ 19 = 2x + $ ← Missing number!
Probably meant to be $ 19 = 2x + 7 $? Or $ 19 = 2x + 1 $? Not clear. Let's assume it's a typo and maybe it's $ 19 = 2x + 7 $? Then:
$ 19 - 7 = 2x $ → $ 12 = 2x $ → $ x = 6 $
But since it's incomplete, we can’t be sure.

Wait — looking again: it says $ 19 = 2x + $, no number. So this equation is incomplete.

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#### 🟢 GREEN Row

9. $ 20 = 8x - 8 $
$ 20 + 8 = 8x $ → $ 28 = 8x $ → $ x = 3.5 $ or $ \frac{7}{2} $

10. $ 4x + 20 = 12 $
$ 4x = -8 $ → $ x = -2 $

11. $ 1 = 3x + 10 $
$ 1 - 10 = 3x $ → $ -9 = 3x $ → $ x = -3 $

12. $ 4x + 12 = ? $ ← Incomplete
Again, no right-hand side. Possibly $ 4x + 12 = 0 $? If so:
$ 4x = -12 $ → $ x = -3 $

But we don’t know.

13. $ 7x - 10 = -17 $
$ 7x = -7 $ → $ x = -1 $

14. $ 12 = 24 - 2x $
$ 2x = 24 - 12 = 12 $ → $ x = 6 $

15. $ 4x + 6 = 0 $
$ 4x = -6 $ → $ x = -1.5 $ or $ -\frac{3}{2} $

16. $ 15 = 3 - ? $ ← Incomplete
Says $ 15 = 3 - $, missing something. Probably $ 15 = 3 - 2x $? Or $ 15 = 3 - x $?
If $ 15 = 3 - x $, then $ x = -12 $, but that seems unlikely.

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Summary of Solvable Equations

Let’s list all equations that are complete and solvable:

| Equation | Solution |
|--------|---------|
| $ 17 = 6x + 5 $ | $ x = 2 $ |
| $ 3x + 12 = 24 $ | $ x = 4 $ |
| $ 14 = 4x - 10 $ | $ x = 6 $ |
| $ 4x - 5 = 5 $ | $ x = 2.5 $ |
| $ 36 = 6x - 24 $ | $ x = 10 $ |
| $ 8x + 6 = 10 $ | $ x = 0.5 $ |
| $ 20 = 8x - 8 $ | $ x = 3.5 $ |
| $ 4x + 20 = 12 $ | $ x = -2 $ |
| $ 1 = 3x + 10 $ | $ x = -3 $ |
| $ 7x - 10 = -17 $ | $ x = -1 $ |
| $ 12 = 24 - 2x $ | $ x = 6 $ |
| $ 4x + 6 = 0 $ | $ x = -1.5 $ |

Now, let’s look at the missing ones:

- $ 4x + 7 = ? $ → missing RHS
- $ 19 = 2x + ? $ → missing constant
- $ 4x + 12 = ? $ → missing RHS
- $ 15 = 3 - ? $ → missing term

These likely have typos or were cut off in the image.

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Possible Interpretation

This type of worksheet often has:

- Students solve each equation.
- Then they use the solution values (like $ x = 2, 4, 6, etc.) to cross off numbers** on a separate list (e.g., numbers 1–12).
- After crossing off, the remaining numbers might spell a word or give a total.

But since no answer list or total instruction is visible, we can only solve what we can.

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Final Answer: Solutions to Complete Equations

Here are the solutions to the complete equations:

| Equation | Solution |
|--------|---------|
| $ 17 = 6x + 5 $ | $ x = 2 $ |
| $ 3x + 12 = 24 $ | $ x = 4 $ |
| $ 14 = 4x - 10 $ | $ x = 6 $ |
| $ 4x - 5 = 5 $ | $ x = 2.5 $ |
| $ 36 = 6x - 24 $ | $ x = 10 $ |
| $ 8x + 6 = 10 $ | $ x = 0.5 $ |
| $ 20 = 8x - 8 $ | $ x = 3.5 $ |
| $ 4x + 20 = 12 $ | $ x = -2 $ |
| $ 1 = 3x + 10 $ | $ x = -3 $ |
| $ 7x - 10 = -17 $ | $ x = -1 $ |
| $ 12 = 24 - 2x $ | $ x = 6 $ |
| $ 4x + 6 = 0 $ | $ x = -1.5 $ |

Note: $ x = 6 $ appears twice.

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Missing Equations – Possible Fixes?

Let’s guess what the missing parts might be:

1. $ 4x + 7 = ? $ → Maybe $ 4x + 7 = 15 $? Then $ 4x = 8 $, $ x = 2 $
2. $ 19 = 2x + ? $ → Maybe $ 19 = 2x + 11 $? Then $ 2x = 8 $, $ x = 4 $
3. $ 4x + 12 = ? $ → Maybe $ 4x + 12 = 0 $? Then $ x = -3 $
4. $ 15 = 3 - ? $ → Maybe $ 15 = 3 - (-12) $? Unlikely. More likely $ 15 = 3 - 2x $? Then $ 2x = -12 $, $ x = -6 $

But without confirmation, we can't be sure.

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Conclusion

✔ Solutions to complete equations are:
$$
x = 2, 4, 6, 2.5, 10, 0.5, 3.5, -2, -3, -1, 6, -1.5
$$

If the task is to find the sum of all solutions, we can compute that:

Sum:
$$
2 + 4 + 6 + 2.5 + 10 + 0.5 + 3.5 + (-2) + (-3) + (-1) + 6 + (-1.5)
$$

Break it down:

Positive: $ 2 + 4 + 6 + 2.5 + 10 + 0.5 + 3.5 + 6 = 34 $
Negative: $ -2 -3 -1 -1.5 = -7.5 $

Total: $ 34 - 7.5 = 26.5 $

So sum of solvable equations' solutions is 26.5

But if the goal is to cross off answers, we need the original list of numbers to cross off.

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Final Answer (Based on Available Data)

> The solutions to the complete equations are:
>
> $ x = 2, 4, 6, 2.5, 10, 0.5, 3.5, -2, -3, -1, 6, -1.5 $
>
> Sum of these solutions: $ \boxed{26.5} $

⚠️ Note: Some equations are incomplete due to missing parts in the image. Please check the original worksheet for missing numbers.

If you can provide the answer list or clarify the task, I can help complete the "cross off" step.