Algebraic equations with solutions for x.

Let's solve each equation in the table and verify whether the given value of $ x $ is correct. We'll go through each one step by step.

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A: $ 3(x + 4) = 4x + 7 $, given $ x = 10 $

Step 1: Expand the left side:
$$
3(x + 4) = 3x + 12
$$

So the equation becomes:
$$
3x + 12 = 4x + 7
$$

Step 2: Subtract $ 3x $ from both sides:
$$
12 = x + 7
$$

Step 3: Subtract 7 from both sides:
$$
x = 5
$$

But the given solution is $ x = 10 $. ✘ Incorrect

✔ Correct answer: $ x = 5 $

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B: $ 2x + 5 = 3(x - 1) $, given $ x = 1.5 $

Step 1: Expand the right side:
$$
3(x - 1) = 3x - 3
$$

Equation:
$$
2x + 5 = 3x - 3
$$

Step 2: Subtract $ 2x $ from both sides:
$$
5 = x - 3
$$

Step 3: Add 3 to both sides:
$$
x = 8
$$

But the given solution is $ x = 1.5 $. ✘ Incorrect

✔ Correct answer: $ x = 8 $

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C: $ 2(3x + 10) = 8x $, given $ x = 3 $

Step 1: Expand the left side:
$$
2(3x + 10) = 6x + 20
$$

Equation:
$$
6x + 20 = 8x
$$

Step 2: Subtract $ 6x $ from both sides:
$$
20 = 2x
$$

Step 3: Divide by 2:
$$
x = 10
$$

But the given solution is $ x = 3 $. ✘ Incorrect

✔ Correct answer: $ x = 10 $

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D: $ 2(4x - 5) = 3x + 10 $, given $ x = 2 $

Step 1: Expand the left side:
$$
2(4x - 5) = 8x - 10
$$

Equation:
$$
8x - 10 = 3x + 10
$$

Step 2: Subtract $ 3x $ from both sides:
$$
5x - 10 = 10
$$

Step 3: Add 10 to both sides:
$$
5x = 20
$$

Step 4: Divide by 5:
$$
x = 4
$$

But the given solution is $ x = 2 $. ✘ Incorrect

✔ Correct answer: $ x = 4 $

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E: $ 2(x + 3) = 3(x + 1) $, given $ x = 2.5 $

Step 1: Expand both sides:
- Left: $ 2(x + 3) = 2x + 6 $
- Right: $ 3(x + 1) = 3x + 3 $

Equation:
$$
2x + 6 = 3x + 3
$$

Step 2: Subtract $ 2x $ from both sides:
$$
6 = x + 3
$$

Step 3: Subtract 3:
$$
x = 3
$$

But the given solution is $ x = 2.5 $. ✘ Incorrect

✔ Correct answer: $ x = 3 $

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F: $ 2(3x + 1) = 3(x - 2) + 29 $, given $ x = 5 $

Step 1: Expand both sides:

Left: $ 2(3x + 1) = 6x + 2 $

Right: $ 3(x - 2) + 29 = 3x - 6 + 29 = 3x + 23 $

Equation:
$$
6x + 2 = 3x + 23
$$

Step 2: Subtract $ 3x $:
$$
3x + 2 = 23
$$

Step 3: Subtract 2:
$$
3x = 21
$$

Step 4: Divide by 3:
$$
x = 7
$$

But the given solution is $ x = 5 $. ✘ Incorrect

✔ Correct answer: $ x = 7 $

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✔ Final Summary:

| Letter | Equation | Given $ x $ | Correct $ x $ | Correct? |
|--------|---------|----------------|------------------|----------|
| A | $ 3(x+4)=4x+7 $ | 10 | 5 | ✘ |
| B | $ 2x+5=3(x-1) $ | 1.5 | 8 | ✘ |
| C | $ 2(3x+10)=8x $ | 3 | 10 | ✘ |
| D | $ 2(4x-5)=3x+10 $ | 2 | 4 | ✘ |
| E | $ 2(x+3)=3(x+1) $ | 2.5 | 3 | ✘ |
| F | $ 2(3x+1)=3(x-2)+29 $ | 5 | 7 | ✘ |

👉 None of the given solutions are correct.

All provided values of $ x $ are incorrect for their respective equations.

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🔍 Bonus: What might be the goal?

The title says "LINK Left & Right", which may suggest a matching activity — perhaps you're supposed to match each equation (left) with the correct solution (right), but currently, all the "right" answers are wrong.

Alternatively, maybe the task is to identify which ones are correct, or to correct the mistakes.

If this is a worksheet where students must verify the solutions, then the conclusion is:

> None of the given solutions are correct. All need correction.

Let me know if you'd like a corrected version of the table!