Let’s solve each expression step by step. We’re simplifying algebraic expressions — that means combining like terms (numbers with numbers, and variables with the same letter).
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1. 2x + 7 + 3x – 2 + 3
Combine x terms: 2x + 3x =
5x
Combine numbers: 7 – 2 + 3 =
8
→
5x + 8
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2. 3x + 9x – 4x – 5
Combine x terms: 3x + 9x – 4x =
8x
Numbers: just –5
→
8x – 5
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3. 5x – x
That’s 5x minus 1x →
4x
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4. 5y + 7y
5 + 7 = 12 →
12y
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5. 7 + 2 + 6y – 2y + 5 – 2y
Numbers: 7 + 2 + 5 =
14
y terms: 6y – 2y – 2y =
2y
→
2y + 14
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6. 2 + 6x + 4 + x
Numbers: 2 + 4 =
6
x terms: 6x + x =
7x
→
7x + 6
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7. 4 + 5y + 6 + 9y
Numbers: 4 + 6 =
10
y terms: 5y + 9y =
14y
→
14y + 10
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8. 3x + 9x – 4x – 5
Same as #2 →
8x – 5
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9. 5 + y – 5 + 2y
Numbers: 5 – 5 =
0
y terms: y + 2y =
3y
→
3y
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10. 3y + 3 + 3y + 1 + 8y + 9
y terms: 3y + 3y + 8y =
14y
Numbers: 3 + 1 + 9 =
13
→
14y + 13
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11. 2 + x – 1 + 4x
x terms: x + 4x =
5x
Numbers: 2 – 1 =
1
→
5x + 1
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12. 8y + 4y
8 + 4 = 12 →
12y
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13. 5y + 5 + 6y + 7 + 7y + 2
y terms: 5y + 6y + 7y =
18y
Numbers: 5 + 7 + 2 =
14
→
18y + 14
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14. 8 + 2x – 7 + 7x
x terms: 2x + 7x =
9x
Numbers: 8 – 7 =
1
→
9x + 1
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15. 9y + 6 – y + 6 + 2y + 3
y terms: 9y – y + 2y =
10y
Numbers: 6 + 6 + 3 =
15
→
10y + 15
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16. 1 + 3y – y
y terms: 3y – y =
2y
Number: 1
→
2y + 1
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17. 7y – 4y + 1 + 6
y terms: 7y – 4y =
3y
Numbers: 1 + 6 =
7
→
3y + 7
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18. 4y + y
4y + 1y =
5y
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19. 9 + 14x – 8x
x terms: 14x – 8x =
6x
Number: 9
→
6x + 9
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20. 16x – 4x – 7x + 13 – 11
x terms: 16x – 4x – 7x =
5x
Numbers: 13 – 11 =
2
→
5x + 2
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Final Answer:
1. 5x + 8
2. 8x – 5
3. 4x
4. 12y
5. 2y + 14
6. 7x + 6
7. 14y + 10
8. 8x – 5
9. 3y
10. 14y + 13
11. 5x + 1
12. 12y
13. 18y + 14
14. 9x + 1
15. 10y + 15
16. 2y + 1
17. 3y + 7
18. 5y
19. 6x + 9
20. 5x + 2
Parent Tip: Review the logic above to help your child master the concept of solving algebraic expressions worksheet.
