Let’s solve each problem step by step. We’re combining like terms — that means we group together the parts with the same variable (like x, y, z) and also combine plain numbers.
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(17) 3y + 12x - y - 3x
→ Group x terms: 12x - 3x =
9x
→ Group y terms: 3y - y =
2y
✔ Final:
9x + 2y
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(18) 2x + 2y - 2x + y
→ Group x terms: 2x - 2x =
0 (they cancel out!)
→ Group y terms: 2y + y =
3y
✔ Final:
3y
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(19) 5x + 6y + 7 + 3x + 2y - 2
→ Group x terms: 5x + 3x =
8x
→ Group y terms: 6y + 2y =
8y
→ Group constants: 7 - 2 =
5
✔ Final:
8x + 8y + 5
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(20) 13x - 5x - 4y + 15 + 3 - 2x
→ Group x terms: 13x - 5x - 2x =
6x
→ Group y terms: -4y (only one) →
-4y
→ Group constants: 15 + 3 =
18
✔ Final:
6x - 4y + 18
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(21) -10x + 2y 5 + 16x - y + 6
*(Note: There’s a space between “2y” and “5”, but it’s likely meant to be part of the expression — so we treat it as: -10x + 2y + 5 + 16x - y + 6)*
→ Group x terms: -10x + 16x =
6x
→ Group y terms: 2y - y =
1y or just
y
→ Group constants: 5 + 6 =
11
✔ Final:
6x + y + 11
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(22) 3x + 4x + 5y + 6y + 7 + 8
→ Group x terms: 3x + 4x =
7x
→ Group y terms: 5y + 6y =
11y
→ Group constants: 7 + 8 =
15
✔ Final:
7x + 11y + 15
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(23) 7x + 7y - 7x + 8y + 12
→ Group x terms: 7x - 7x =
0 (cancel out)
→ Group y terms: 7y + 8y =
15y
→ Constants:
12
✔ Final:
15y + 12
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Final Answer:
(17) 9x + 2y
(18) 3y
(19) 8x + 8y + 5
(20) 6x - 4y + 18
(21) 6x + y + 11
(22) 7x + 11y + 15
(23) 15y + 12
Parent Tip: Review the logic above to help your child master the concept of pre algebra worksheet answers.
