This worksheet provides 20 practice problems for solving linear algebraic equations with variables on both sides.

Let's solve each of these algebraic equations step by step. The goal is to isolate the variable on one side of the equation.

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1. $ 15z - 35 = -34 + 14z $

Step 1: Subtract $14z$ from both sides:
$$
15z - 14z - 35 = -34
\Rightarrow z - 35 = -34
$$

Step 2: Add 35 to both sides:
$$
z = -34 + 35 = 1
$$

✔ Answer: $ z = 1 $

---

2. $ 15b - 4 = 53 + 14b $

Step 1: Subtract $14b$ from both sides:
$$
15b - 14b - 4 = 53
\Rightarrow b - 4 = 53
$$

Step 2: Add 4 to both sides:
$$
b = 57
$$

✔ Answer: $ b = 57 $

---

3. $ -3d + 38 = 76 - 4d $

Step 1: Add $4d$ to both sides:
$$
-3d + 4d + 38 = 76
\Rightarrow d + 38 = 76
$$

Step 2: Subtract 38:
$$
d = 76 - 38 = 38
$$

✔ Answer: $ d = 38 $

---

4. $ 22u + 26 = 77 + 21u $

Step 1: Subtract $21u$ from both sides:
$$
22u - 21u + 26 = 77
\Rightarrow u + 26 = 77
$$

Step 2: Subtract 26:
$$
u = 77 - 26 = 51
$$

✔ Answer: $ u = 51 $

---

5. $ 16q + 7 = 43 + 15q $

Step 1: Subtract $15q$:
$$
16q - 15q + 7 = 43
\Rightarrow q + 7 = 43
$$

Step 2: Subtract 7:
$$
q = 36
$$

✔ Answer: $ q = 36 $

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6. $ 19x - 48 = 2 + 18x $

Step 1: Subtract $18x$:
$$
19x - 18x - 48 = 2
\Rightarrow x - 48 = 2
$$

Step 2: Add 48:
$$
x = 50
$$

✔ Answer: $ x = 50 $

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7. $ 5x - 36 = -2 + 4x $

Step 1: Subtract $4x$:
$$
5x - 4x - 36 = -2
\Rightarrow x - 36 = -2
$$

Step 2: Add 36:
$$
x = 34
$$

✔ Answer: $ x = 34 $

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8. $ -3x + 19 = 72 - 4x $

Step 1: Add $4x$ to both sides:
$$
-3x + 4x + 19 = 72
\Rightarrow x + 19 = 72
$$

Step 2: Subtract 19:
$$
x = 53
$$

✔ Answer: $ x = 53 $

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9. $ 17m - 22 = -5 + 16m $

Step 1: Subtract $16m$:
$$
17m - 16m - 22 = -5
\Rightarrow m - 22 = -5
$$

Step 2: Add 22:
$$
m = 17
$$

✔ Answer: $ m = 17 $

---

10. $ 17x + 39 = 64 + 16x $

Step 1: Subtract $16x$:
$$
17x - 16x + 39 = 64
\Rightarrow x + 39 = 64
$$

Step 2: Subtract 39:
$$
x = 25
$$

✔ Answer: $ x = 25 $

---

11. $ 19c - 29 = 3 + 18c $

Step 1: Subtract $18c$:
$$
19c - 18c - 29 = 3
\Rightarrow c - 29 = 3
$$

Step 2: Add 29:
$$
c = 32
$$

✔ Answer: $ c = 32 $

---

12. $ 5r - 37 = -10 + 4r $

Step 1: Subtract $4r$:
$$
5r - 4r - 37 = -10
\Rightarrow r - 37 = -10
$$

Step 2: Add 37:
$$
r = 27
$$

✔ Answer: $ r = 27 $

---

13. $ 8g + 14 = 45 + 7g $

Step 1: Subtract $7g$:
$$
8g - 7g + 14 = 45
\Rightarrow g + 14 = 45
$$

Step 2: Subtract 14:
$$
g = 31
$$

✔ Answer: $ g = 31 $

---

14. $ 11r + 45 = 60 + 10r $

Step 1: Subtract $10r$:
$$
11r - 10r + 45 = 60
\Rightarrow r + 45 = 60
$$

Step 2: Subtract 45:
$$
r = 15
$$

✔ Answer: $ r = 15 $

---

15. $ -2e - 33 = 41 - 3e $

Step 1: Add $3e$ to both sides:
$$
-2e + 3e - 33 = 41
\Rightarrow e - 33 = 41
$$

Step 2: Add 33:
$$
e = 74
$$

✔ Answer: $ e = 74 $

---

16. $ 10b + 11 = 28 + 9b $

Step 1: Subtract $9b$:
$$
10b - 9b + 11 = 28
\Rightarrow b + 11 = 28
$$

Step 2: Subtract 11:
$$
b = 17
$$

✔ Answer: $ b = 17 $

---

17. $ 10f + 37 = 38 + 9f $

Step 1: Subtract $9f$:
$$
10f - 9f + 37 = 38
\Rightarrow f + 37 = 38
$$

Step 2: Subtract 37:
$$
f = 1
$$

✔ Answer: $ f = 1 $

---

18. $ -2f - 28 = 38 - 3f $

Step 1: Add $3f$ to both sides:
$$
-2f + 3f - 28 = 38
\Rightarrow f - 28 = 38
$$

Step 2: Add 28:
$$
f = 66
$$

✔ Answer: $ f = 66 $

---

19. $ 10k - 8 = 30 + 9k $

Step 1: Subtract $9k$:
$$
10k - 9k - 8 = 30
\Rightarrow k - 8 = 30
$$

Step 2: Add 8:
$$
k = 38
$$

✔ Answer: $ k = 38 $

---

20. $ 14h + 41 = 98 + 13h $

Step 1: Subtract $13h$:
$$
14h - 13h + 41 = 98
\Rightarrow h + 41 = 98
$$

Step 2: Subtract 41:
$$
h = 57
$$

✔ Answer: $ h = 57 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ z = 1 $ |
| 2 | $ b = 57 $ |
| 3 | $ d = 38 $ |
| 4 | $ u = 51 $ |
| 5 | $ q = 36 $ |
| 6 | $ x = 50 $ |
| 7 | $ x = 34 $ |
| 8 | $ x = 53 $ |
| 9 | $ m = 17 $ |
| 10 | $ x = 25 $ |
| 11 | $ c = 32 $ |
| 12 | $ r = 27 $ |
| 13 | $ g = 31 $ |
| 14 | $ r = 15 $ |
| 15 | $ e = 74 $ |
| 16 | $ b = 17 $ |
| 17 | $ f = 1 $ |
| 18 | $ f = 66 $ |
| 19 | $ k = 38 $ |
| 20 | $ h = 57 $ |

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🔍 Summary of Strategy:

For all problems:
1. Move variables to one side, constants to the other.
2. Combine like terms.
3. Solve for the variable by dividing or adding/subtracting.

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