Answer :
Certainly! Let’s carefully and clearly match the expressions with equal values.
First, let’s clarify which expressions are equivalent to each other.
1. [tex]\(12n - 4 - 4n \cdot 8n + 1 \cdot 3 + 3n + 4 + 2n\)[/tex]
- This simplifies to: [tex]\(-32n^2 + 17n + 3\)[/tex]
2. [tex]\(3n + 5\)[/tex]
- This simplifies to: [tex]\(3n + 5\)[/tex]
3. [tex]\(n + n + n + 5\)[/tex]
- This simplifies to: [tex]\(3n + 5\)[/tex]
4. [tex]\(5 - 10n + 2 + 15n\)[/tex]
- This simplifies to: [tex]\(5n + 7\)[/tex]
5. [tex]\(-4n - 4 + 4n\)[/tex]
- This simplifies to: [tex]\(-4\)[/tex]
6. [tex]\(4 + 4n + 4 + 4n\)[/tex]
- This simplifies to: [tex]\(8n + 8\)[/tex]
7. [tex]\(-8n + 8\)[/tex]
- This simplifies to: [tex]\(8 - 8n\)[/tex]
8. [tex]\(4(2n - 1)\)[/tex]
- This simplifies to: [tex]\(8n - 4\)[/tex]
9. [tex]\(-5n + 7\)[/tex]
- This simplifies to: [tex]\(7 - 5n\)[/tex]
10. [tex]\(4n + 5 + n + 2\)[/tex]
- This simplifies to: [tex]\(5n + 7\)[/tex]
11. [tex]\(2n + 5 + n\)[/tex]
- This simplifies to: [tex]\(3n + 5\)[/tex]
12. [tex]\(8 - n + 9n\)[/tex]
- This simplifies to: [tex]\(8n + 8\)[/tex]
13. [tex]\(3n + 5 + 5n - 1\)[/tex]
- This simplifies to: [tex]\(8n + 4\)[/tex]
Now, match the equal values:
1. [tex]\(12n - 4 - 4n \cdot 8n + 1 \cdot 3 + 3n + 4 + 2n\)[/tex]
- No match with any other expression.
2. [tex]\(3n + 5\)[/tex] [tex]\(\bullet\)[/tex]
- Matches with:
- [tex]\(n + n + n + 5\)[/tex] [tex]\(\bullet\)[/tex]
- [tex]\(2n + 5 + n\)[/tex]
Use Blue lines to connect these.
3. [tex]\(5 - 10n + 2 + 15n\)[/tex]
- Matches with:
- [tex]\(4n + 5 + n + 2\)[/tex]
Use Red lines to connect these.
4. [tex]\(-4n - 4 + 4n\)[/tex]
- No match with any other expression.
5. [tex]\(4 + 4n + 4 + 4n\)[/tex]
- Matches with:
- [tex]\(8 - n + 9n\)[/tex]
Use Green lines to connect these.
6. [tex]\(-8n + 8\)[/tex]
- No match with any other expression.
7. [tex]\(4(2n - 1)\)[/tex] [tex]\(\circ\)[/tex]
- No match with any other expression.
8. [tex]\(-5n + 7\)[/tex]
- No match with any other expression.
9. [tex]\(3n + 5\)[/tex] [tex]\(\bullet\)[/tex]
- Already matched.
10. [tex]\(4n + 5 + n + 2\)[/tex] [tex]\(\circ\)[/tex]
- Matches with:
- [tex]\(5 - 10n + 2 + 15n\)[/tex]
Use Red lines to connect these.
11. [tex]\(2n + 5 + n\)[/tex]
- Already matched.
12. [tex]\(8 - n + 9n\)[/tex]
- Already matched.
13. [tex]\(3n + 5 + 5n - 1\)[/tex]
- No match with any other expression.
So your final matching looks like this using straight lines:
- Blue Line: [tex]\(3n + 5\)[/tex] [tex]\(\bullet\)[/tex] [tex]\(n+n+n+5\)[/tex] and [tex]\(2n+5+n\)[/tex]
- Red Line: [tex]\(5 - 10n + 2 + 15n\)[/tex] → [tex]\(4n + 5 + n + 2\)[/tex]
- Green Line: [tex]\(4 + 4n + 4 + 4n\)[/tex] → [tex]\(8 - n + 9n\)[/tex]
Remember to use different color lines to connect the matching expressions on your paper or diagram to clearly illustrate the equal values connected by straight lines.
First, let’s clarify which expressions are equivalent to each other.
1. [tex]\(12n - 4 - 4n \cdot 8n + 1 \cdot 3 + 3n + 4 + 2n\)[/tex]
- This simplifies to: [tex]\(-32n^2 + 17n + 3\)[/tex]
2. [tex]\(3n + 5\)[/tex]
- This simplifies to: [tex]\(3n + 5\)[/tex]
3. [tex]\(n + n + n + 5\)[/tex]
- This simplifies to: [tex]\(3n + 5\)[/tex]
4. [tex]\(5 - 10n + 2 + 15n\)[/tex]
- This simplifies to: [tex]\(5n + 7\)[/tex]
5. [tex]\(-4n - 4 + 4n\)[/tex]
- This simplifies to: [tex]\(-4\)[/tex]
6. [tex]\(4 + 4n + 4 + 4n\)[/tex]
- This simplifies to: [tex]\(8n + 8\)[/tex]
7. [tex]\(-8n + 8\)[/tex]
- This simplifies to: [tex]\(8 - 8n\)[/tex]
8. [tex]\(4(2n - 1)\)[/tex]
- This simplifies to: [tex]\(8n - 4\)[/tex]
9. [tex]\(-5n + 7\)[/tex]
- This simplifies to: [tex]\(7 - 5n\)[/tex]
10. [tex]\(4n + 5 + n + 2\)[/tex]
- This simplifies to: [tex]\(5n + 7\)[/tex]
11. [tex]\(2n + 5 + n\)[/tex]
- This simplifies to: [tex]\(3n + 5\)[/tex]
12. [tex]\(8 - n + 9n\)[/tex]
- This simplifies to: [tex]\(8n + 8\)[/tex]
13. [tex]\(3n + 5 + 5n - 1\)[/tex]
- This simplifies to: [tex]\(8n + 4\)[/tex]
Now, match the equal values:
1. [tex]\(12n - 4 - 4n \cdot 8n + 1 \cdot 3 + 3n + 4 + 2n\)[/tex]
- No match with any other expression.
2. [tex]\(3n + 5\)[/tex] [tex]\(\bullet\)[/tex]
- Matches with:
- [tex]\(n + n + n + 5\)[/tex] [tex]\(\bullet\)[/tex]
- [tex]\(2n + 5 + n\)[/tex]
Use Blue lines to connect these.
3. [tex]\(5 - 10n + 2 + 15n\)[/tex]
- Matches with:
- [tex]\(4n + 5 + n + 2\)[/tex]
Use Red lines to connect these.
4. [tex]\(-4n - 4 + 4n\)[/tex]
- No match with any other expression.
5. [tex]\(4 + 4n + 4 + 4n\)[/tex]
- Matches with:
- [tex]\(8 - n + 9n\)[/tex]
Use Green lines to connect these.
6. [tex]\(-8n + 8\)[/tex]
- No match with any other expression.
7. [tex]\(4(2n - 1)\)[/tex] [tex]\(\circ\)[/tex]
- No match with any other expression.
8. [tex]\(-5n + 7\)[/tex]
- No match with any other expression.
9. [tex]\(3n + 5\)[/tex] [tex]\(\bullet\)[/tex]
- Already matched.
10. [tex]\(4n + 5 + n + 2\)[/tex] [tex]\(\circ\)[/tex]
- Matches with:
- [tex]\(5 - 10n + 2 + 15n\)[/tex]
Use Red lines to connect these.
11. [tex]\(2n + 5 + n\)[/tex]
- Already matched.
12. [tex]\(8 - n + 9n\)[/tex]
- Already matched.
13. [tex]\(3n + 5 + 5n - 1\)[/tex]
- No match with any other expression.
So your final matching looks like this using straight lines:
- Blue Line: [tex]\(3n + 5\)[/tex] [tex]\(\bullet\)[/tex] [tex]\(n+n+n+5\)[/tex] and [tex]\(2n+5+n\)[/tex]
- Red Line: [tex]\(5 - 10n + 2 + 15n\)[/tex] → [tex]\(4n + 5 + n + 2\)[/tex]
- Green Line: [tex]\(4 + 4n + 4 + 4n\)[/tex] → [tex]\(8 - n + 9n\)[/tex]
Remember to use different color lines to connect the matching expressions on your paper or diagram to clearly illustrate the equal values connected by straight lines.
