Two step linear equations - Free Printable

Let’s solve each equation step by step. We’ll isolate the variable (like x, y, z, etc.) on one side of the equation by doing the same thing to both sides — like subtracting or dividing.

We’ll go in order from 1 to 48. Since there are many, I’ll show a few examples first, then list all answers at the end with quick steps for each.

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Example 1: 2x + 3 = 11

Step 1: Subtract 3 from both sides
→ 2x = 8

Step 2: Divide both sides by 2
→ x = 4

✔ Answer: x = 4

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Example 5: 2y + 5 = 17

Step 1: Subtract 5 from both sides
→ 2y = 12

Step 2: Divide by 2
→ y = 6

✔ Answer: y = 6

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Example 9: 7 = 2x - 7

Step 1: Add 7 to both sides
→ 14 = 2x

Step 2: Divide by 2
→ x = 7

✔ Answer: x = 7

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Now let’s do them all quickly and carefully:

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1. 2x + 3 = 11 → 2x=8 → x=4
2. 3x + 1 = 10 → 3x=9 → x=3
3. 4x - 2 = 2 → 4x=4 → x=1
4. 5x - 7 = 3 → 5x=10 → x=2
5. 2y + 5 = 17 → 2y=12 → y=6
6. 3z - 4 = 17 → 3z=21 → z=7
7. 8x + 10 = 34 → 8x=24 → x=3
8. 21 = 5 + 4x → 16=4x → x=4
9. 7 = 2x - 7 → 14=2x → x=7
10. 8 + 3a = 8 → 3a=0 → a=0
11. 5b - 4 = 31 → 5b=35 → b=7
12. 17 = 7x - 11 → 28=7x → x=4

13. 6c + 4 = 46 → 6c=42 → c=7
14. 9d + 11 = 47 → 9d=36 → d=4
15. 5x - 8 = 31 → 5x=39 → x=39/5 (improper fraction)
16. 2f + 5 = 16 → 2f=11 → f=11/2
17. 3h - 2 = 12 → 3h=14 → h=14/3
18. 4k + 1 = 2 → 4k=1 → k=1/4 ← Wait! This is not positive integer coefficient? But problem says “positive integer coefficient of the unknown” — k has coefficient 4, which is fine. Answer can be fraction.
But let’s check: 4k + 1 = 2 → 4k = 1 → k = 1/4 ✔
19. 5p + 3 = 15 → 5p=12 → p=12/5
20. 2q - 7 = 10 → 2q=17 → q=17/2
21. 6r - 2 = 3 → 6r=5 → r=5/6
22. 4s + 6 = 20 → 4s=14 → s=14/4 = 7/2 (simplify)
23. 6x - 5 = 10 → 6x=15 → x=15/6 = 5/2
24. 10x - 4 = 9 → 10x=13 → x=13/10
25. 2t + 4 = 12 → 2t=8 → t=4
26. 4u + 8 = 16 → 4u=8 → u=2
27. 6v + 5 = 47 → 6v=42 → v=7
28. 3 + 5x = 3 → 5x=0 → x=0
29. 6x + 2 = 74 → 6x=72 → x=12
30. 15 = 6w + 9 → 6=6w → w=1
31. 6x + 9 = 75 → 6x=66 → x=11
32. 26 = 8 + 6x → 18=6x → x=3
33. 5x + 3 = 53 → 5x=50 → x=10
34. 54 = 7x + 5 → 49=7x → x=7
35. 23 = 7 + 2x → 16=2x → x=8
36. 10 + 7x = 45 → 7x=35 → x=5
37. 2m - 4 = -2 → 2m=2 → m=1
38. 5n - 20 = 0 → 5n=20 → n=4
39. 4x - 9 = -17 → 4x=-8 → x=-2 ← negative answer, but allowed
40. 47 = 5p - 18 → 65=5p → p=13
41. -36 = 7r - 8 → -28=7r → r=-4
42. 2a - 9 = -19 → 2a=-10 → a=-5
43. -15 = 4x - 15 → 0=4x → x=0
44. -8 = 9b - 35 → 27=9b → b=3
45. 10 = 10c - 20 → 30=10c → c=3
46. 12x - 17 = 31 → 12x=48 → x=4
47. 25x - 9 = -84 → 25x=-75 → x=-3
48. 32x - 15 = -79 → 32x=-64 → x=-2

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All done! Let me double-check a tricky ones:

- #15: 5x - 8 = 31 → 5x = 39 → x = 39/5 ✔️
- #18: 4k + 1 = 2 → 4k = 1 → k = 1/4 ✔️
- #43: -15 = 4x - 15 → add 15 to both sides → 0 = 4x → x=0 ✔️
- #47: 25x - 9 = -84 → 25x = -75 → x = -3 ✔️

Everything checks out.

Final Answer:
1. x = 4
2. x = 3
3. x = 1
4. x = 2
5. y = 6
6. z = 7
7. x = 3
8. x = 4
9. x = 7
10. a = 0
11. b = 7
12. x = 4
13. c = 7
14. d = 4
15. x = 39/5
16. f = 11/2
17. h = 14/3
18. k = 1/4
19. p = 12/5
20. q = 17/2
21. r = 5/6
22. s = 7/2
23. x = 5/2
24. x = 13/10
25. t = 4
26. u = 2
27. v = 7
28. x = 0
29. x = 12
30. w = 1
31. x = 11
32. x = 3
33. x = 10
34. x = 7
35. x = 8
36. x = 5
37. m = 1
38. n = 4
39. x = -2
40. p = 13
41. r = -4
42. a = -5
43. x = 0
44. b = 3
45. c = 3
46. x = 4
47. x = -3
48. x = -2