Pre-Algebra | AIAN - RM 302 - Free Printable
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Step-by-step solution for: Pre-Algebra | AIAN - RM 302
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Show Answer Key & Explanations
Step-by-step solution for: Pre-Algebra | AIAN - RM 302
You’ve uploaded a math worksheet with two sections:
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## SECTION 1: Identify the terms, like terms, coefficients, and constants in each expression.
We’ll go one by one.
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- Terms: 3, 7x, 3x, x
- Like terms: 7x, 3x, x (all are x-terms)
- Coefficients: 7 (for 7x), 3 (for 3x), 1 (for x — implied coefficient)
- Constants: 3
✔ *Note: The constant is the term without a variable.*
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- Terms: y, 3y, 8y, 2
- Like terms: y, 3y, 8y (all are y-terms)
- Coefficients: 1 (for y), 3, 8
- Constants: 2
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- Terms: 2a, 5c, -a, 6a
- Like terms: 2a, -a, 6a (all are a-terms); 5c is alone
- Coefficients: 2 (for 2a), 5 (for 5c), -1 (for -a), 6 (for 6a)
- Constants: None (no number without a variable)
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- Terms: 5c, -2d, 3d, -d
- Like terms: -2d, 3d, -d (all are d-terms); 5c is alone
- Coefficients: 5 (for 5c), -2, 3, -1 (for -d)
- Constants: None
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- Terms: 6m, -2n, 7
- Like terms: None — all variables are different or constant
- Coefficients: 6 (for 6m), -2 (for -2n)
- Constants: 7
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- Terms: 7x, -3y, 3z, -2
- Like terms: None — all variables different or constant
- Coefficients: 7, -3, 3
- Constants: -2
---
## SECTION 2: Simplify each expression.
We combine like terms — terms with the same variable and exponent.
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→ Distribute: 3b + 6 + 2b
→ Combine: (3b + 2b) + 6 = 5b + 6
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→ Distribute: 5x + 15 + 8x
→ Combine: (5x + 8x) + 15 = 13x + 15
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→ Distribute: -3a - 6 - a
→ Combine: (-3a - a) - 6 = -4a - 6
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→ Distribute: -2x - 6 + 2x
→ Combine: (-2x + 2x) - 6 = 0 - 6 = -6
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→ Distribute: 4x - 8 - 4x
→ Combine: (4x - 4x) - 8 = 0 - 8 = -8
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→ Distribute: 8a - 2a + 14
→ Combine: (8a - 2a) + 14 = 6a + 14
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→ Combine m-terms: (6m + 10m) + 2n = 16m + 2n
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→ Combine y-terms: (-2y + 3y) + x = y + x or x + y
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→ Distribute: c + 2d - 10c
→ Combine c-terms: (c - 10c) + 2d = -9c + 2d
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## ✔ Final Summary:
You now have:
- For problems 17–22: Identified terms, like terms, coefficients, constants.
- For problems 23–49: Simplified expressions by combining like terms and distributing where needed.
Let me know if you’d like these written out in a printable format or need explanations for any specific step!
---
## SECTION 1: Identify the terms, like terms, coefficients, and constants in each expression.
We’ll go one by one.
---
17. 3 + 7x + 3x + x
- Terms: 3, 7x, 3x, x
- Like terms: 7x, 3x, x (all are x-terms)
- Coefficients: 7 (for 7x), 3 (for 3x), 1 (for x — implied coefficient)
- Constants: 3
✔ *Note: The constant is the term without a variable.*
---
18. y + 3y + 8y + 2
- Terms: y, 3y, 8y, 2
- Like terms: y, 3y, 8y (all are y-terms)
- Coefficients: 1 (for y), 3, 8
- Constants: 2
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19. 2a + 5c - a + 6a
- Terms: 2a, 5c, -a, 6a
- Like terms: 2a, -a, 6a (all are a-terms); 5c is alone
- Coefficients: 2 (for 2a), 5 (for 5c), -1 (for -a), 6 (for 6a)
- Constants: None (no number without a variable)
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20. 5c - 2d + 3d - d
- Terms: 5c, -2d, 3d, -d
- Like terms: -2d, 3d, -d (all are d-terms); 5c is alone
- Coefficients: 5 (for 5c), -2, 3, -1 (for -d)
- Constants: None
---
21. 6m - 2n + 7
- Terms: 6m, -2n, 7
- Like terms: None — all variables are different or constant
- Coefficients: 6 (for 6m), -2 (for -2n)
- Constants: 7
---
22. 7x - 3y + 3z - 2
- Terms: 7x, -3y, 3z, -2
- Like terms: None — all variables different or constant
- Coefficients: 7, -3, 3
- Constants: -2
---
## SECTION 2: Simplify each expression.
We combine like terms — terms with the same variable and exponent.
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23. 2x + 5x = 7x
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24. 7b + 2b = 9b
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25. y + 10y = 11y
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26. 5y + y = 6y
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27. 2a + 3 + 5a = (2a + 5a) + 3 = 7a + 3
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28. 4 + 2m + m = 4 + (2m + m) = 4 + 3m
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29. 2y + 8 + 5y + 1 = (2y + 5y) + (8 + 1) = 7y + 9
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30. 8x + 5 + 7 + 2x = (8x + 2x) + (5 + 7) = 10x + 12
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31. 5x - 3x = 2x
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32. 10b - 2b = 8b
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33. 4y - 5y = -y
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34. r - 3r = -2r
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35. 8 + x - 5x = 8 + (x - 5x) = 8 - 4x
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36. 6x + 4 - 7x = (6x - 7x) + 4 = -x + 4
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37. 8y - 7 + 7 = 8y + (-7 + 7) = 8y + 0 = 8y
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38. 9x + 2 - 2 = 9x + (2 - 2) = 9x + 0 = 9x
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39. 2x + 3 - 3x + 9 = (2x - 3x) + (3 + 9) = -x + 12
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40. 5t - 3 - t + 2 = (5t - t) + (-3 + 2) = 4t - 1
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41. 3(b + 2) + 2b
→ Distribute: 3b + 6 + 2b
→ Combine: (3b + 2b) + 6 = 5b + 6
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42. 5(x + 3) + 8x
→ Distribute: 5x + 15 + 8x
→ Combine: (5x + 8x) + 15 = 13x + 15
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43. -3(a + 2) - a
→ Distribute: -3a - 6 - a
→ Combine: (-3a - a) - 6 = -4a - 6
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44. -2(x + 3) + 2x
→ Distribute: -2x - 6 + 2x
→ Combine: (-2x + 2x) - 6 = 0 - 6 = -6
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45. 4x - 4(2 + x)
→ Distribute: 4x - 8 - 4x
→ Combine: (4x - 4x) - 8 = 0 - 8 = -8
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46. 8a - 2(a - 7)
→ Distribute: 8a - 2a + 14
→ Combine: (8a - 2a) + 14 = 6a + 14
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47. 6m + 2n + 10m
→ Combine m-terms: (6m + 10m) + 2n = 16m + 2n
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48. -2y + x + 3y
→ Combine y-terms: (-2y + 3y) + x = y + x or x + y
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49. c + 2(d - 5c)
→ Distribute: c + 2d - 10c
→ Combine c-terms: (c - 10c) + 2d = -9c + 2d
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## ✔ Final Summary:
You now have:
- For problems 17–22: Identified terms, like terms, coefficients, constants.
- For problems 23–49: Simplified expressions by combining like terms and distributing where needed.
Let me know if you’d like these written out in a printable format or need explanations for any specific step!
Parent Tip: Review the logic above to help your child master the concept of pre algebra worksheet with answer key.
