Question

Use algebra tiles to find (5x+7)–(x+6).
x
x
x
x
x
1
1
1
1
1
1
1
–
x
1
1
1
1
1
1
Combine like terms. For example, write 3 instead of 1 + 1 + 1.

Answer 1

To solve \((5x + 7) - (x + 6)\) using algebra tiles, we can visualize the tiles as follows:

1. **Represent the expressions using tiles**:
- For \(5x + 7\), you have:
- 5 tiles for \(x\) (representing \(5x\))
- 7 tiles for \(1\) (representing \(+7\))
- For \(x + 6\), you have:
- 1 tile for \(x\) (representing \(x\))
- 6 tiles for \(1\) (representing \(+6\))

2. **Set up the equation**:
Visualize the first expression \(5x + 7\) and then subtract the second expression \(x + 6\):
\[
(5x + 7) - (x + 6)
\]

3. **Subtracting the tiles**:
- First, take away 1 \(x\) tile from the 5 \(x\) tiles:
- You have \(5x - x = 4x\).
- Next, remove 6 unit tiles from the 7 unit tiles:
- You have \(7 - 6 = 1\).

4. **Combine the results**:
After removing the tiles, you end up with:
- 4 tiles for \(x\) (which represents \(4x\))
- 1 tile for \(1\) (which represents \(1\))

Putting this together, the final expression after combining like terms from the initial subtraction is:
\[
4x + 1
\]

So, \((5x + 7) - (x + 6) = 4x + 1\).