To model the equation [tex]\( 9x + 2 = 8x + (-6) \)[/tex] with algebra tiles, we can break down the components of each side of the equation as follows:
### For the left side of the equation ([tex]\( 9x + 2 \)[/tex]):
1. Positive [tex]\( x \)[/tex]-tiles:
- The term [tex]\( 9x \)[/tex] indicates that we have 9 positive [tex]\( x \)[/tex]-tiles.
2. Positive unit tiles:
- The constant term [tex]\( 2 \)[/tex] indicates that we have 2 positive unit tiles.
### For the right side of the equation ([tex]\( 8x + (-6) \)[/tex]):
1. Positive [tex]\( x \)[/tex]-tiles:
- The term [tex]\( 8x \)[/tex] indicates that we have 8 positive [tex]\( x \)[/tex]-tiles.
2. Negative unit tiles:
- The term [tex]\( -6 \)[/tex] indicates that we have 6 negative unit tiles.
So, if we lay out the algebra tiles, we have:
#### For the left side of the equation:
- 9 positive [tex]\( x \)[/tex]-tiles.
- 2 positive unit tiles.
#### For the right side of the equation:
- 8 positive [tex]\( x \)[/tex]-tiles.
- 6 negative unit tiles.
Thus, the equation [tex]\( 9x + 2 = 8x + (-6) \)[/tex] can be represented with algebra tiles as follows:
For the left side of the equation:
- 9 positive [tex]\( x \)[/tex]-tiles
- 2 positive unit tiles
For the right side of the equation:
- 8 positive [tex]\( x \)[/tex]-tiles
- 6 negative unit tiles
