To determine which equation Karina represented using the algebra tiles, we need to analyze the options provided:
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4x + 5 = -6: This suggests 4 tiles representing x and 5 unit tiles on the left side equals -6, which would involve having negative unit tiles on the right side.
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5x - 4 = -6: This suggests 5 tiles representing x and taking away 4 unit tiles on the left side equals -6 on the right side.
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5x + 4 = -6: This indicates 5 tiles representing x and adding 4 unit tiles on the left side equals -6, which implies having negative unit tiles on the right side.
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4x - 5 = 6: This implies 4 tiles representing x and taking away 5 unit tiles on the left side equals 6 on the right side.
Based on standard practices of representing equations with algebra tiles, typically, the count of x-tiles and unit tiles should match the equation's balance.
If we analyze commonly used representations:
- If we have 5 tiles indicating xs and need to adjust for a certain number of unit tiles, one would expect to properly balance the units on both sides of the equation described.
Assuming that Karina's algebra tiles indicated that there were more positive x-contributions as seen in option 2 (5x - 4 = -6), it represents having excess x-tiles sufficient to bear the removal of 4 units equaling to a deficit on the right side, which aligns into standard forms of algebra equations.
To clarify, it's presumed that the concrete setup of the tiles would illustrate a clear representation.
Thus, the most fitting representation of the equation will likely be 5x - 4 = -6.
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