Algebra worksheet for solving linear equations, Set 2.

Let's solve each equation step by step. These are all linear equations in one variable, and we'll solve for $ x $ using algebraic operations.

---

1) $ 4x + 17 = 49 $

Step 1: Subtract 17 from both sides
$$
4x = 49 - 17 = 32
$$

Step 2: Divide both sides by 4
$$
x = \frac{32}{4} = 8
$$

✔ Answer: $ x = 8 $

---

2) $ 2x + 11 = 27 $

Step 1: Subtract 11 from both sides
$$
2x = 27 - 11 = 16
$$

Step 2: Divide by 2
$$
x = \frac{16}{2} = 8
$$

✔ Answer: $ x = 8 $

---

3) $ 6x - 23 = 31 $

Step 1: Add 23 to both sides
$$
6x = 31 + 23 = 54
$$

Step 2: Divide by 6
$$
x = \frac{54}{6} = 9
$$

✔ Answer: $ x = 9 $

---

4) $ 7x + 2 = 16 $

Step 1: Subtract 2 from both sides
$$
7x = 16 - 2 = 14
$$

Step 2: Divide by 7
$$
x = \frac{14}{7} = 2
$$

✔ Answer: $ x = 2 $

---

5) $ 3x + 10 = 37 $

Step 1: Subtract 10 from both sides
$$
3x = 37 - 10 = 27
$$

Step 2: Divide by 3
$$
x = \frac{27}{3} = 9
$$

✔ Answer: $ x = 9 $

---

6) $ 7x - 24 = 25 $

Step 1: Add 24 to both sides
$$
7x = 25 + 24 = 49
$$

Step 2: Divide by 7
$$
x = \frac{49}{7} = 7
$$

✔ Answer: $ x = 7 $

---

7) $ 2x - 1 = 5 $

Step 1: Add 1 to both sides
$$
2x = 5 + 1 = 6
$$

Step 2: Divide by 2
$$
x = \frac{6}{2} = 3
$$

✔ Answer: $ x = 3 $

---

8) $ 5x - 2 = 33 $

Step 1: Add 2 to both sides
$$
5x = 33 + 2 = 35
$$

Step 2: Divide by 5
$$
x = \frac{35}{5} = 7
$$

✔ Answer: $ x = 7 $

---

9) $ 5x + 34 = 74 $

Step 1: Subtract 34 from both sides
$$
5x = 74 - 34 = 40
$$

Step 2: Divide by 5
$$
x = \frac{40}{5} = 8
$$

✔ Answer: $ x = 8 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $ x = 8 $ |
| 2) | $ x = 8 $ |
| 3) | $ x = 9 $ |
| 4) | $ x = 2 $ |
| 5) | $ x = 9 $ |
| 6) | $ x = 7 $ |
| 7) | $ x = 3 $ |
| 8) | $ x = 7 $ |
| 9) | $ x = 8 $ |

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🔍 Summary of Method:

For each equation:
1. Isolate the term with $ x $ by moving constants to the other side.
2. Use addition/subtraction first, then multiplication/division.
3. Always perform the same operation on both sides to keep the equation balanced.

Let me know if you'd like this as a printable answer sheet!