Math worksheet featuring ten algebra problems where students must rearrange equations to make the number 2 the subject, accompanied by two worked examples.

The task is to rearrange each equation so that the number 2 is isolated on one side, i.e., solve for 2 (or "get [2] on its own"), by reversing the operations step-by-step, similar to how it's shown in the examples.

We’ll go through each of the 10 equations and rearrange them to express 2 = ..., following the logic from the examples.

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🔧 Strategy:

We are not solving for a variable like $ x $; we are treating "2" as the unknown and rearranging the equation so that 2 appears alone on one side.

We'll use inverse operations:
- If something is added, subtract it.
- If multiplied, divide.
- If divided, multiply.
- If in parentheses or denominator, isolate step by step.

Let’s do each one.

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(1) $ 5 \times 2 - 3 = 7 $

Step-by-step:
$$
5 \times 2 - 3 = 7
$$
Add 3 to both sides:
$$
5 \times 2 = 10
$$
Divide both sides by 5:
$$
2 = \frac{10}{5} = 2
$$

✔ So: $ \boxed{2 = \frac{7 + 3}{5}} $

---

(2) $ \frac{6}{2} + 7 = 10 $

$$
\frac{6}{2} + 7 = 10
$$
Subtract 7:
$$
\frac{6}{2} = 3
$$
Now: $ \frac{6}{2} = 3 $ → $ 2 = \frac{6}{3} $

✔ So: $ \boxed{2 = \frac{6}{10 - 7}} $

---

(3) $ \frac{63}{5 + 2} - 1 = 8 $

$$
\frac{63}{5 + 2} - 1 = 8
$$
Add 1:
$$
\frac{63}{5 + 2} = 9
$$
So: $ \frac{63}{7} = 9 $ → $ 5 + 2 = \frac{63}{9} = 7 $

Then: $ 2 = 7 - 5 = 2 $

✔ So: $ \boxed{2 = \frac{63}{9} - 5} $ → but better to write directly:

From $ \frac{63}{5 + 2} = 9 $, then:
$$
5 + 2 = \frac{63}{9} = 7 \Rightarrow 2 = 7 - 5 = 2
$$

But we want an expression:
$ 2 = \frac{63}{9} - 5 $

But let's keep it algebraic:
$$
\frac{63}{5 + 2} = 9 \Rightarrow 5 + 2 = \frac{63}{9} = 7 \Rightarrow 2 = 7 - 5
$$

So: $ \boxed{2 = \frac{63}{9} - 5} $

Alternatively, since $ 9 = 8 + 1 $, we can say:
$$
\frac{63}{5 + 2} = 8 + 1 \Rightarrow 5 + 2 = \frac{63}{8 + 1}
\Rightarrow 2 = \frac{63}{8 + 1} - 5
$$

✔ Final answer: $ \boxed{2 = \frac{63}{8 + 1} - 5} $

---

(4) $ 4(5 - 2) + 8 = 20 $

$$
4(5 - 2) + 8 = 20
$$
Subtract 8:
$$
4(5 - 2) = 12
$$
Divide by 4:
$$
5 - 2 = 3
\Rightarrow 2 = 5 - 3 = 2
$$

So: $ 5 - 2 = \frac{12}{4} = 3 \Rightarrow 2 = 5 - \frac{12}{4} $

But $ 12 = 20 - 8 $, so:

$$
2 = 5 - \frac{20 - 8}{4}
$$

✔ $ \boxed{2 = 5 - \frac{20 - 8}{4}} $

---

(5) $ 10 - \frac{20}{2 + 3} = 6 $

$$
10 - \frac{20}{2 + 3} = 6
$$
Subtract 10:
$$
- \frac{20}{2 + 3} = -4
\Rightarrow \frac{20}{2 + 3} = 4
\Rightarrow 2 + 3 = \frac{20}{4} = 5
\Rightarrow 2 = 5 - 3 = 2
$$

So: $ 2 + 3 = \frac{20}{4} = 5 \Rightarrow 2 = \frac{20}{4} - 3 $

But $ 4 = 10 - 6 $, so:

$$
2 = \frac{20}{10 - 6} - 3
$$

✔ $ \boxed{2 = \frac{20}{10 - 6} - 3} $

---

(6) $ \frac{70}{2 \times 3 + 4} + 6 = 13 $

$$
\frac{70}{2 \times 3 + 4} + 6 = 13
$$
Subtract 6:
$$
\frac{70}{2 \times 3 + 4} = 7
$$
So:
$$
2 \times 3 + 4 = \frac{70}{7} = 10
\Rightarrow 6 + 4 = 10 \Rightarrow 6 = 6
\Rightarrow 2 = \frac{10 - 4}{3} = \frac{6}{3} = 2
$$

So:
$$
2 \times 3 = 10 - 4 = 6 \Rightarrow 2 = \frac{10 - 4}{3}
$$

And $ 10 = \frac{70}{7} $, $ 7 = 13 - 6 $, so:

$$
2 = \frac{\frac{70}{13 - 6} - 4}{3}
$$

✔ $ \boxed{2 = \frac{\frac{70}{13 - 6} - 4}{3}} $

---

(7) $ \frac{48}{3 + \frac{10}{2}} = 6 $

$$
\frac{48}{3 + \frac{10}{2}} = 6
$$
Multiply both sides by denominator:
$$
48 = 6 \left(3 + \frac{10}{2}\right)
\Rightarrow 48 = 18 + \frac{60}{2} = 18 + 30 = 48
$$

Better: $ 3 + \frac{10}{2} = \frac{48}{6} = 8 $

So:
$$
3 + \frac{10}{2} = 8 \Rightarrow \frac{10}{2} = 5 \Rightarrow 2 = \frac{10}{5} = 2
$$

But we need to isolate 2.

We have:
$$
3 + \frac{10}{2} = 8 \Rightarrow \frac{10}{2} = 5 \Rightarrow 2 = \frac{10}{5}
$$

But $ 8 = \frac{48}{6} $, $ 6 $ is given, so:

$$
\frac{10}{2} = \frac{48}{6} - 3 = 8 - 3 = 5
\Rightarrow 2 = \frac{10}{\frac{48}{6} - 3}
$$

✔ $ \boxed{2 = \frac{10}{\frac{48}{6} - 3}} $

---

(8) $ 9 - \frac{24}{2 \times 3} = 5 $

$$
9 - \frac{24}{2 \times 3} = 5
\Rightarrow \frac{24}{2 \times 3} = 4
\Rightarrow 2 \times 3 = \frac{24}{4} = 6
\Rightarrow 2 = \frac{6}{3} = 2
$$

So:
$$
2 \times 3 = \frac{24}{4} = 6 \Rightarrow 2 = \frac{6}{3}
$$

But $ 4 = 9 - 5 $, so:

$$
2 = \frac{24}{9 - 5} \div 3 = \frac{24}{3(9 - 5)}
\Rightarrow 2 = \frac{24}{3(9 - 5)} = \frac{24}{3 \times 4} = \frac{24}{12} = 2
$$

Wait — better:

From $ \frac{24}{2 \times 3} = 4 $, so:

$$
2 \times 3 = \frac{24}{4} = 6 \Rightarrow 2 = \frac{6}{3}
$$

But $ 6 = \frac{24}{4} $, $ 4 = 9 - 5 $, so:

$$
2 = \frac{24}{3(9 - 5)}
$$

✔ $ \boxed{2 = \frac{24}{3(9 - 5)}} $

---

(9) $ 3\left(\frac{56}{9 - 2} + 4\right) + 7 = 43 $

$$
3\left(\frac{56}{9 - 2} + 4\right) + 7 = 43
$$
Subtract 7:
$$
3\left(\frac{56}{9 - 2} + 4\right) = 36
$$
Divide by 3:
$$
\frac{56}{9 - 2} + 4 = 12
\Rightarrow \frac{56}{9 - 2} = 8
\Rightarrow 9 - 2 = \frac{56}{8} = 7
\Rightarrow 2 = 9 - 7 = 2
$$

So:
$$
9 - 2 = \frac{56}{8} = 7 \Rightarrow 2 = 9 - \frac{56}{8}
$$

But $ 8 = 12 - 4 $, and $ 12 = \frac{36}{3} $, $ 36 = 43 - 7 $

So:
$$
8 = \frac{43 - 7}{3} - 4 = \frac{36}{3} - 4 = 12 - 4 = 8
$$

Thus:
$$
2 = 9 - \frac{56}{\frac{43 - 7}{3} - 4}
$$

✔ $ \boxed{2 = 9 - \frac{56}{\frac{43 - 7}{3} - 4}} $

---

(10) $ 3\left(4 + \frac{18}{5 - 2}\right) - 9 = 21 $

$$
3\left(4 + \frac{18}{5 - 2}\right) - 9 = 21
$$
Add 9:
$$
3\left(4 + \frac{18}{5 - 2}\right) = 30
$$
Divide by 3:
$$
4 + \frac{18}{5 - 2} = 10
\Rightarrow \frac{18}{5 - 2} = 6
\Rightarrow 5 - 2 = \frac{18}{6} = 3
\Rightarrow 2 = 5 - 3 = 2
$$

So:
$$
5 - 2 = \frac{18}{6} = 3 \Rightarrow 2 = 5 - \frac{18}{6}
$$

But $ 6 = 10 - 4 $, $ 10 = \frac{30}{3} $, $ 30 = 21 + 9 $

So:
$$
6 = \frac{21 + 9}{3} - 4 = \frac{30}{3} - 4 = 10 - 4 = 6
$$

Thus:
$$
2 = 5 - \frac{18}{\frac{21 + 9}{3} - 4}
$$

✔ $ \boxed{2 = 5 - \frac{18}{\frac{21 + 9}{3} - 4}} $

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## ✔ Final Answers (All Rearranged to Isolate [2]):

| Equation | Rearranged Form |
|--------|----------------|
| (1) | $ 2 = \frac{7 + 3}{5} $ |
| (2) | $ 2 = \frac{6}{10 - 7} $ |
| (3) | $ 2 = \frac{63}{8 + 1} - 5 $ |
| (4) | $ 2 = 5 - \frac{20 - 8}{4} $ |
| (5) | $ 2 = \frac{20}{10 - 6} - 3 $ |
| (6) | $ 2 = \frac{\frac{70}{13 - 6} - 4}{3} $ |
| (7) | $ 2 = \frac{10}{\frac{48}{6} - 3} $ |
| (8) | $ 2 = \frac{24}{3(9 - 5)} $ |
| (9) | $ 2 = 9 - \frac{56}{\frac{43 - 7}{3} - 4} $ |
| (10) | $ 2 = 5 - \frac{18}{\frac{21 + 9}{3} - 4} $ |

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📌 Summary:

We used reverse operations and substitution to isolate the number 2 in each equation, just like in the examples. The key idea is:
- Work backwards from the result.
- Undo addition/subtraction, multiplication/division step-by-step.
- Express intermediate values in terms of known numbers.

This type of problem builds algebraic reasoning and manipulation skills.