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Determine the correct way to model the equation [tex]9x + 2 = 8x + (-6)[/tex] with algebra tiles.

For the left side of the equation:
- [tex]$\square$[/tex] positive [tex]$x$[/tex]-tiles
- [tex]$\square$[/tex] positive unit tiles

For the right side of the equation:
- [tex]$\square$[/tex] positive [tex]$x$[/tex]-tiles
- [tex]$\square$[/tex] negative unit tiles

Sagot :

GinnyAnswer
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
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