Worksheet with algebra equations and a video link for solving equations with letters on both sides.

Let's solve each of these equations step by step. These are linear equations with variables on both sides, so the goal is to isolate the variable $ x $ on one side.

---

General Strategy:

1. Move all terms with $ x $ to one side.
2. Move constant terms to the other side.
3. Simplify and solve for $ x $.

We’ll go through each part:

---

(a) $ 4x + 1 = 2x + 7 $

Subtract $ 2x $ from both sides:
$$
4x - 2x + 1 = 7 \Rightarrow 2x + 1 = 7
$$

Subtract 1 from both sides:
$$
2x = 6
$$

Divide by 2:
$$
x = 3
$$

✔ Answer: $ x = 3 $

---

(b) $ 5x + 4 = 3x + 16 $

Subtract $ 3x $ from both sides:
$$
2x + 4 = 16
$$

Subtract 4:
$$
2x = 12
$$

Divide by 2:
$$
x = 6
$$

✔ Answer: $ x = 6 $

---

(c) $ 2x + 8 = x + 12 $

Subtract $ x $ from both sides:
$$
x + 8 = 12
$$

Subtract 8:
$$
x = 4
$$

✔ Answer: $ x = 4 $

---

(d) $ 7x + 1 = 2x + 46 $

Subtract $ 2x $:
$$
5x + 1 = 46
$$

Subtract 1:
$$
5x = 45
$$

Divide by 5:
$$
x = 9
$$

✔ Answer: $ x = 9 $

---

(e) $ 6x - 3 = 2x + 13 $

Subtract $ 2x $:
$$
4x - 3 = 13
$$

Add 3:
$$
4x = 16
$$

Divide by 4:
$$
x = 4
$$

✔ Answer: $ x = 4 $

---

(f) $ 9x - 10 = 7x + 24 $

Subtract $ 7x $:
$$
2x - 10 = 24
$$

Add 10:
$$
2x = 34
$$

Divide by 2:
$$
x = 17
$$

✔ Answer: $ x = 17 $

---

(g) $ 2x + 21 = 4x + 5 $

Subtract $ 2x $:
$$
21 = 2x + 5
$$

Subtract 5:
$$
16 = 2x
$$

Divide by 2:
$$
x = 8
$$

✔ Answer: $ x = 8 $

---

(h) $ x + 2 = 5x - 2 $

Subtract $ x $:
$$
2 = 4x - 2
$$

Add 2:
$$
4 = 4x
$$

Divide by 4:
$$
x = 1
$$

✔ Answer: $ x = 1 $

---

(i) $ 6x - 9 = 4x - 1 $

Subtract $ 4x $:
$$
2x - 9 = -1
$$

Add 9:
$$
2x = 8
$$

Divide by 2:
$$
x = 4
$$

✔ Answer: $ x = 4 $

---

(j) $ 5x + 2 = 16 - 2x $

Add $ 2x $ to both sides:
$$
7x + 2 = 16
$$

Subtract 2:
$$
7x = 14
$$

Divide by 7:
$$
x = 2
$$

✔ Answer: $ x = 2 $

---

(k) $ 3x - 1 = 23 - x $

Add $ x $ to both sides:
$$
4x - 1 = 23
$$

Add 1:
$$
4x = 24
$$

Divide by 4:
$$
x = 6
$$

✔ Answer: $ x = 6 $

---

(l) $ 6x + 8 = 38 - 4x $

Add $ 4x $ to both sides:
$$
10x + 8 = 38
$$

Subtract 8:
$$
10x = 30
$$

Divide by 10:
$$
x = 3
$$

✔ Answer: $ x = 3 $

---

(m) $ 80 - x = 8x - 1 $

Add $ x $ to both sides:
$$
80 = 9x - 1
$$

Add 1:
$$
81 = 9x
$$

Divide by 9:
$$
x = 9
$$

✔ Answer: $ x = 9 $

---

(n) $ 2x + 7 = 17 - 8x $

Add $ 8x $ to both sides:
$$
10x + 7 = 17
$$

Subtract 7:
$$
10x = 10
$$

Divide by 10:
$$
x = 1
$$

✔ Answer: $ x = 1 $

---

(o) $ 15 - x = 27 - 3x $

Add $ 3x $ to both sides:
$$
15 + 2x = 27
$$

Subtract 15:
$$
2x = 12
$$

Divide by 2:
$$
x = 6
$$

✔ Answer: $ x = 6 $

---

(p) $ 12x - 20 = 15x - 38 $

Subtract $ 12x $:
$$
-20 = 3x - 38
$$

Add 38:
$$
18 = 3x
$$

Divide by 3:
$$
x = 6
$$

✔ Answer: $ x = 6 $

---

(q) $ 35x + 10 = 20x + 175 $

Subtract $ 20x $:
$$
15x + 10 = 175
$$

Subtract 10:
$$
15x = 165
$$

Divide by 15:
$$
x = 11
$$

✔ Answer: $ x = 11 $

---

(r) $ 14x = 2x + 60 $

Subtract $ 2x $:
$$
12x = 60
$$

Divide by 12:
$$
x = 5
$$

✔ Answer: $ x = 5 $

---

✔ Final Answers Summary:

| Part | Answer |
|------|--------|
| (a) | $ x = 3 $ |
| (b) | $ x = 6 $ |
| (c) | $ x = 4 $ |
| (d) | $ x = 9 $ |
| (e) | $ x = 4 $ |
| (f) | $ x = 17 $ |
| (g) | $ x = 8 $ |
| (h) | $ x = 1 $ |
| (i) | $ x = 4 $ |
| (j) | $ x = 2 $ |
| (k) | $ x = 6 $ |
| (l) | $ x = 3 $ |
| (m) | $ x = 9 $ |
| (n) | $ x = 1 $ |
| (o) | $ x = 6 $ |
| (p) | $ x = 6 $ |
| (q) | $ x = 11 $ |
| (r) | $ x = 5 $ |

---

Let me know if you'd like a video explanation or printable version!