MATH 10 Combining Like Terms Worksheet Solutions - Kuta Software ... - Free Printable
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Step-by-step solution for: MATH 10 Combining Like Terms Worksheet Solutions - Kuta Software ...
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Show Answer Key & Explanations
Step-by-step solution for: MATH 10 Combining Like Terms Worksheet Solutions - Kuta Software ...
Let’s solve each problem step by step. We’ll go one at a time, carefully.
---
1. 3x + 5 = 20
Subtract 5 from both sides:
→ 3x = 15
Divide both sides by 3:
→ x = 5
✔ Check: 3(5) + 5 = 15 + 5 = 20 → Correct.
---
2. 7 - 2y = 1
Subtract 7 from both sides:
→ -2y = -6
Divide both sides by -2:
→ y = 3
✔ Check: 7 - 2(3) = 7 - 6 = 1 → Correct.
---
3. 4a - 8 = 12
Add 8 to both sides:
→ 4a = 20
Divide by 4:
→ a = 5
✔ Check: 4(5) - 8 = 20 - 8 = 12 → Correct.
---
4. 6b + 3 = 27
Subtract 3:
→ 6b = 24
Divide by 6:
→ b = 4
✔ Check: 6(4) + 3 = 24 + 3 = 27 → Correct.
---
5. 9 - c = 4
Subtract 9:
→ -c = -5
Multiply both sides by -1:
→ c = 5
✔ Check: 9 - 5 = 4 → Correct.
---
6. 2d + 7 = 15
Subtract 7:
→ 2d = 8
Divide by 2:
→ d = 4
✔ Check: 2(4) + 7 = 8 + 7 = 15 → Correct.
---
7. 5e - 10 = 0
Add 10:
→ 5e = 10
Divide by 5:
→ e = 2
✔ Check: 5(2) - 10 = 10 - 10 = 0 → Correct.
---
8. 3f + 4 = 19
Subtract 4:
→ 3f = 15
Divide by 3:
→ f = 5
✔ Check: 3(5) + 4 = 15 + 4 = 19 → Correct.
---
9. 8g - 2 = 14
Add 2:
→ 8g = 16
Divide by 8:
→ g = 2
✔ Check: 8(2) - 2 = 16 - 2 = 14 → Correct.
---
10. 10h + 5 = 35
Subtract 5:
→ 10h = 30
Divide by 10:
→ h = 3
✔ Check: 10(3) + 5 = 30 + 5 = 35 → Correct.
---
11. 2(x + 3) = 16
Distribute the 2:
→ 2x + 6 = 16
Subtract 6:
→ 2x = 10
Divide by 2:
→ x = 5
✔ Check: 2(5 + 3) = 2(8) = 16 → Correct.
---
12. 3(y - 2) = 9
Distribute the 3:
→ 3y - 6 = 9
Add 6:
→ 3y = 15
Divide by 3:
→ y = 5
✔ Check: 3(5 - 2) = 3(3) = 9 → Correct.
---
13. 4(a + 1) = 20
Distribute:
→ 4a + 4 = 20
Subtract 4:
→ 4a = 16
Divide by 4:
→ a = 4
✔ Check: 4(4 + 1) = 4(5) = 20 → Correct.
---
14. 5(b - 3) = 10
Distribute:
→ 5b - 15 = 10
Add 15:
→ 5b = 25
Divide by 5:
→ b = 5
✔ Check: 5(5 - 3) = 5(2) = 10 → Correct.
---
15. 2(c + 4) = 18
Distribute:
→ 2c + 8 = 18
Subtract 8:
→ 2c = 10
Divide by 2:
→ c = 5
✔ Check: 2(5 + 4) = 2(9) = 18 → Correct.
---
16. 3(d - 1) = 12
Distribute:
→ 3d - 3 = 12
Add 3:
→ 3d = 15
Divide by 3:
→ d = 5
✔ Check: 3(5 - 1) = 3(4) = 12 → Correct.
---
17. 4(e + 2) = 24
Distribute:
→ 4e + 8 = 24
Subtract 8:
→ 4e = 16
Divide by 4:
→ e = 4
✔ Check: 4(4 + 2) = 4(6) = 24 → Correct.
---
18. 5(f - 2) = 15
Distribute:
→ 5f - 10 = 15
Add 10:
→ 5f = 25
Divide by 5:
→ f = 5
✔ Check: 5(5 - 2) = 5(3) = 15 → Correct.
---
19. 2(g + 5) = 16
Distribute:
→ 2g + 10 = 16
Subtract 10:
→ 2g = 6
Divide by 2:
→ g = 3
✔ Check: 2(3 + 5) = 2(8) = 16 → Correct.
---
20. 3(h - 4) = 9
Distribute:
→ 3h - 12 = 9
Add 12:
→ 3h = 21
Divide by 3:
→ h = 7
✔ Check: 3(7 - 4) = 3(3) = 9 → Correct.
---
21. 4x - 3 = 2x + 5
Subtract 2x from both sides:
→ 2x - 3 = 5
Add 3:
→ 2x = 8
Divide by 2:
→ x = 4
✔ Check: Left: 4(4) - 3 = 16 - 3 = 13; Right: 2(4) + 5 = 8 + 5 = 13 → Equal → Correct.
---
22. 5y + 2 = 3y - 8
Subtract 3y:
→ 2y + 2 = -8
Subtract 2:
→ 2y = -10
Divide by 2:
→ y = -5
✔ Check: Left: 5(-5) + 2 = -25 + 2 = -23; Right: 3(-5) - 8 = -15 - 8 = -23 → Correct.
---
23. 6a - 4 = 2a + 12
Subtract 2a:
→ 4a - 4 = 12
Add 4:
→ 4a = 16
Divide by 4:
→ a = 4
✔ Check: Left: 6(4) - 4 = 24 - 4 = 20; Right: 2(4) + 12 = 8 + 12 = 20 → Correct.
---
24. 7b + 1 = 3b - 11
Subtract 3b:
→ 4b + 1 = -11
Subtract 1:
→ 4b = -12
Divide by 4:
→ b = -3
✔ Check: Left: 7(-3) + 1 = -21 + 1 = -20; Right: 3(-3) - 11 = -9 - 11 = -20 → Correct.
---
25. 8c - 5 = 4c + 7
Subtract 4c:
→ 4c - 5 = 7
Add 5:
→ 4c = 12
Divide by 4:
→ c = 3
✔ Check: Left: 8(3) - 5 = 24 - 5 = 19; Right: 4(3) + 7 = 12 + 7 = 19 → Correct.
---
26. 9d + 2 = 5d - 10
Subtract 5d:
→ 4d + 2 = -10
Subtract 2:
→ 4d = -12
Divide by 4:
→ d = -3
✔ Check: Left: 9(-3) + 2 = -27 + 2 = -25; Right: 5(-3) - 10 = -15 - 10 = -25 → Correct.
---
27. 10e - 6 = 6e + 10
Subtract 6e:
→ 4e - 6 = 10
Add 6:
→ 4e = 16
Divide by 4:
→ e = 4
✔ Check: Left: 10(4) - 6 = 40 - 6 = 34; Right: 6(4) + 10 = 24 + 10 = 34 → Correct.
---
28. 3(f + 2) = 2(f - 1)
Distribute both sides:
Left: 3f + 6
Right: 2f - 2
So: 3f + 6 = 2f - 2
Subtract 2f:
→ f + 6 = -2
Subtract 6:
→ f = -8
✔ Check: Left: 3(-8 + 2) = 3(-6) = -18; Right: 2(-8 - 1) = 2(-9) = -18 → Correct.
---
29. 4(g - 3) = 3(g + 1)
Distribute:
Left: 4g - 12
Right: 3g + 3
So: 4g - 12 = 3g + 3
Subtract 3g:
→ g - 12 = 3
Add 12:
→ g = 15
✔ Check: Left: 4(15 - 3) = 4(12) = 48; Right: 3(15 + 1) = 3(16) = 48 → Correct.
---
30. 5(h + 1) = 2(h - 4)
Distribute:
Left: 5h + 5
Right: 2h - 8
So: 5h + 5 = 2h - 8
Subtract 2h:
→ 3h + 5 = -8
Subtract 5:
→ 3h = -13
Divide by 3:
→ h = -13/3 or -4⅓
✔ Check: Left: 5(-13/3 + 1) = 5(-10/3) = -50/3
Right: 2(-13/3 - 4) = 2(-13/3 - 12/3) = 2(-25/3) = -50/3 → Correct.
---
Final Answer:
1. x = 5
2. y = 3
3. a = 5
4. b = 4
5. c = 5
6. d = 4
7. e = 2
8. f = 5
9. g = 2
10. h = 3
11. x = 5
12. y = 5
13. a = 4
14. b = 5
15. c = 5
16. d = 5
17. e = 4
18. f = 5
19. g = 3
20. h = 7
21. x = 4
22. y = -5
23. a = 4
24. b = -3
25. c = 3
26. d = -3
27. e = 4
28. f = -8
29. g = 15
30. h = -13/3 (or -4⅓)
---
1. 3x + 5 = 20
Subtract 5 from both sides:
→ 3x = 15
Divide both sides by 3:
→ x = 5
✔ Check: 3(5) + 5 = 15 + 5 = 20 → Correct.
---
2. 7 - 2y = 1
Subtract 7 from both sides:
→ -2y = -6
Divide both sides by -2:
→ y = 3
✔ Check: 7 - 2(3) = 7 - 6 = 1 → Correct.
---
3. 4a - 8 = 12
Add 8 to both sides:
→ 4a = 20
Divide by 4:
→ a = 5
✔ Check: 4(5) - 8 = 20 - 8 = 12 → Correct.
---
4. 6b + 3 = 27
Subtract 3:
→ 6b = 24
Divide by 6:
→ b = 4
✔ Check: 6(4) + 3 = 24 + 3 = 27 → Correct.
---
5. 9 - c = 4
Subtract 9:
→ -c = -5
Multiply both sides by -1:
→ c = 5
✔ Check: 9 - 5 = 4 → Correct.
---
6. 2d + 7 = 15
Subtract 7:
→ 2d = 8
Divide by 2:
→ d = 4
✔ Check: 2(4) + 7 = 8 + 7 = 15 → Correct.
---
7. 5e - 10 = 0
Add 10:
→ 5e = 10
Divide by 5:
→ e = 2
✔ Check: 5(2) - 10 = 10 - 10 = 0 → Correct.
---
8. 3f + 4 = 19
Subtract 4:
→ 3f = 15
Divide by 3:
→ f = 5
✔ Check: 3(5) + 4 = 15 + 4 = 19 → Correct.
---
9. 8g - 2 = 14
Add 2:
→ 8g = 16
Divide by 8:
→ g = 2
✔ Check: 8(2) - 2 = 16 - 2 = 14 → Correct.
---
10. 10h + 5 = 35
Subtract 5:
→ 10h = 30
Divide by 10:
→ h = 3
✔ Check: 10(3) + 5 = 30 + 5 = 35 → Correct.
---
11. 2(x + 3) = 16
Distribute the 2:
→ 2x + 6 = 16
Subtract 6:
→ 2x = 10
Divide by 2:
→ x = 5
✔ Check: 2(5 + 3) = 2(8) = 16 → Correct.
---
12. 3(y - 2) = 9
Distribute the 3:
→ 3y - 6 = 9
Add 6:
→ 3y = 15
Divide by 3:
→ y = 5
✔ Check: 3(5 - 2) = 3(3) = 9 → Correct.
---
13. 4(a + 1) = 20
Distribute:
→ 4a + 4 = 20
Subtract 4:
→ 4a = 16
Divide by 4:
→ a = 4
✔ Check: 4(4 + 1) = 4(5) = 20 → Correct.
---
14. 5(b - 3) = 10
Distribute:
→ 5b - 15 = 10
Add 15:
→ 5b = 25
Divide by 5:
→ b = 5
✔ Check: 5(5 - 3) = 5(2) = 10 → Correct.
---
15. 2(c + 4) = 18
Distribute:
→ 2c + 8 = 18
Subtract 8:
→ 2c = 10
Divide by 2:
→ c = 5
✔ Check: 2(5 + 4) = 2(9) = 18 → Correct.
---
16. 3(d - 1) = 12
Distribute:
→ 3d - 3 = 12
Add 3:
→ 3d = 15
Divide by 3:
→ d = 5
✔ Check: 3(5 - 1) = 3(4) = 12 → Correct.
---
17. 4(e + 2) = 24
Distribute:
→ 4e + 8 = 24
Subtract 8:
→ 4e = 16
Divide by 4:
→ e = 4
✔ Check: 4(4 + 2) = 4(6) = 24 → Correct.
---
18. 5(f - 2) = 15
Distribute:
→ 5f - 10 = 15
Add 10:
→ 5f = 25
Divide by 5:
→ f = 5
✔ Check: 5(5 - 2) = 5(3) = 15 → Correct.
---
19. 2(g + 5) = 16
Distribute:
→ 2g + 10 = 16
Subtract 10:
→ 2g = 6
Divide by 2:
→ g = 3
✔ Check: 2(3 + 5) = 2(8) = 16 → Correct.
---
20. 3(h - 4) = 9
Distribute:
→ 3h - 12 = 9
Add 12:
→ 3h = 21
Divide by 3:
→ h = 7
✔ Check: 3(7 - 4) = 3(3) = 9 → Correct.
---
21. 4x - 3 = 2x + 5
Subtract 2x from both sides:
→ 2x - 3 = 5
Add 3:
→ 2x = 8
Divide by 2:
→ x = 4
✔ Check: Left: 4(4) - 3 = 16 - 3 = 13; Right: 2(4) + 5 = 8 + 5 = 13 → Equal → Correct.
---
22. 5y + 2 = 3y - 8
Subtract 3y:
→ 2y + 2 = -8
Subtract 2:
→ 2y = -10
Divide by 2:
→ y = -5
✔ Check: Left: 5(-5) + 2 = -25 + 2 = -23; Right: 3(-5) - 8 = -15 - 8 = -23 → Correct.
---
23. 6a - 4 = 2a + 12
Subtract 2a:
→ 4a - 4 = 12
Add 4:
→ 4a = 16
Divide by 4:
→ a = 4
✔ Check: Left: 6(4) - 4 = 24 - 4 = 20; Right: 2(4) + 12 = 8 + 12 = 20 → Correct.
---
24. 7b + 1 = 3b - 11
Subtract 3b:
→ 4b + 1 = -11
Subtract 1:
→ 4b = -12
Divide by 4:
→ b = -3
✔ Check: Left: 7(-3) + 1 = -21 + 1 = -20; Right: 3(-3) - 11 = -9 - 11 = -20 → Correct.
---
25. 8c - 5 = 4c + 7
Subtract 4c:
→ 4c - 5 = 7
Add 5:
→ 4c = 12
Divide by 4:
→ c = 3
✔ Check: Left: 8(3) - 5 = 24 - 5 = 19; Right: 4(3) + 7 = 12 + 7 = 19 → Correct.
---
26. 9d + 2 = 5d - 10
Subtract 5d:
→ 4d + 2 = -10
Subtract 2:
→ 4d = -12
Divide by 4:
→ d = -3
✔ Check: Left: 9(-3) + 2 = -27 + 2 = -25; Right: 5(-3) - 10 = -15 - 10 = -25 → Correct.
---
27. 10e - 6 = 6e + 10
Subtract 6e:
→ 4e - 6 = 10
Add 6:
→ 4e = 16
Divide by 4:
→ e = 4
✔ Check: Left: 10(4) - 6 = 40 - 6 = 34; Right: 6(4) + 10 = 24 + 10 = 34 → Correct.
---
28. 3(f + 2) = 2(f - 1)
Distribute both sides:
Left: 3f + 6
Right: 2f - 2
So: 3f + 6 = 2f - 2
Subtract 2f:
→ f + 6 = -2
Subtract 6:
→ f = -8
✔ Check: Left: 3(-8 + 2) = 3(-6) = -18; Right: 2(-8 - 1) = 2(-9) = -18 → Correct.
---
29. 4(g - 3) = 3(g + 1)
Distribute:
Left: 4g - 12
Right: 3g + 3
So: 4g - 12 = 3g + 3
Subtract 3g:
→ g - 12 = 3
Add 12:
→ g = 15
✔ Check: Left: 4(15 - 3) = 4(12) = 48; Right: 3(15 + 1) = 3(16) = 48 → Correct.
---
30. 5(h + 1) = 2(h - 4)
Distribute:
Left: 5h + 5
Right: 2h - 8
So: 5h + 5 = 2h - 8
Subtract 2h:
→ 3h + 5 = -8
Subtract 5:
→ 3h = -13
Divide by 3:
→ h = -13/3 or -4⅓
✔ Check: Left: 5(-13/3 + 1) = 5(-10/3) = -50/3
Right: 2(-13/3 - 4) = 2(-13/3 - 12/3) = 2(-25/3) = -50/3 → Correct.
---
Final Answer:
1. x = 5
2. y = 3
3. a = 5
4. b = 4
5. c = 5
6. d = 4
7. e = 2
8. f = 5
9. g = 2
10. h = 3
11. x = 5
12. y = 5
13. a = 4
14. b = 5
15. c = 5
16. d = 5
17. e = 4
18. f = 5
19. g = 3
20. h = 7
21. x = 4
22. y = -5
23. a = 4
24. b = -3
25. c = 3
26. d = -3
27. e = 4
28. f = -8
29. g = 15
30. h = -13/3 (or -4⅓)
Parent Tip: Review the logic above to help your child master the concept of combining like terms worksheet pre algebra.
