Let’s simplify each pair expression and match them to the corresponding tiles.
Tiles:
1. [tex]\(10x + 6\)[/tex]
2. [tex]\(2x - 8\)[/tex]
3. [tex]\(\sin(3x) - 5\)[/tex]
4. [tex]\(2x + 14\)[/tex]
5. [tex]\(2x + 6\)[/tex]
6. [tex]\(10x + 14\)[/tex]
Pairs:
1. [tex]\[(-2x + 4) + 2(2x + 1)\][/tex]
2. [tex]\[2(3x + 5) - 4(x - 1)\][/tex]
3. [tex]\[2(x - 7) + (8x + 20)\][/tex]
Step-by-Step Simplification and Matching:
### Pair 1: [tex]\[(-2x + 4) + 2(2x + 1)\][/tex]
1. Distribute the 2:
[tex]\[2 \cdot 2x + 2 \cdot 1 = 4x + 2\][/tex]
2. Combine like terms:
[tex]\[(-2x + 4) + (4x + 2) = -2x + 4 + 4x + 2\][/tex]
3. Simplify:
[tex]\[-2x + 4x + 4 + 2 = 2x + 6\][/tex]
So, Pair 1 simplifies to: [tex]\(2x + 6\)[/tex]
### Pair 2: [tex]\[2(3x + 5) - 4(x - 1)\][/tex]
1. Distribute the 2 and the -4:
[tex]\[2 \cdot 3x + 2 \cdot 5 = 6x + 10\][/tex]
[tex]\[-4 \cdot x + (-4) \cdot (-1) = -4x + 4\][/tex]
2. Combine like terms:
[tex]\[6x + 10 - 4x + 4\][/tex]
3. Simplify:
[tex]\[6x - 4x + 10 + 4 = 2x + 14\][/tex]
So, Pair 2 simplifies to: [tex]\(2x + 14\)[/tex]
### Pair 3: [tex]\[2(x - 7) + (8x + 20)\][/tex]
1. Distribute the 2:
[tex]\[2 \cdot x + 2 \cdot (-7) = 2x - 14\][/tex]
2. Combine like terms:
[tex]\[(2x - 14) + (8x + 20)\][/tex]
3. Simplify:
[tex]\[2x + 8x - 14 + 20 = 10x + 6\][/tex]
So, Pair 3 simplifies to: [tex]\(10x + 6\)[/tex]
### Matching
Now, let's match the simplified pairs with the given tiles:
1. Tile: [tex]\(10x + 6\)[/tex] → Pair 3
2. Tile: [tex]\(2x - 8\)[/tex] → No match
3. Tile: [tex]\(\sin(3x) - 5\)[/tex] → No match
4. Tile: [tex]\(2x + 14\)[/tex] → Pair 2
5. Tile: [tex]\(2x + 6\)[/tex] → Pair 1
6. Tile: [tex]\(10x + 14\)[/tex] → No match
Thus, the matching is as follows:
- [tex]\(10x + 6\)[/tex] matches with [tex]\(2(x - 7) + (8x + 20)\)[/tex]
- [tex]\(2x - 8\)[/tex] has no match
- [tex]\(\sin(3x) - 5\)[/tex] has no match
- [tex]\(2x + 14\)[/tex] matches with [tex]\(2(3x + 5) - 4(x - 1)\)[/tex]
- [tex]\(2x + 6\)[/tex] matches with [tex]\( (-2x + 4) + 2(2x + 1)\)[/tex]
- [tex]\(10x + 14\)[/tex] has no match
