If Tillie is solving an equation for \( x \) and her first step is to subtract 8 from both sides, the equation must originally include a positive 8 on one side. This means that the equation she is solving must be in a form where subtracting 8 leads directly to a simpler form.
Let's analyze the options:
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\( 12 = -x + 8 \)
- Subtracting 8 from both sides results in \( 12 - 8 = -x \), or \( 4 = -x \). This is a valid step.
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\( 12 - x = 8 \)
- Subtracting 8 from both sides results in \( 12 - x - 8 = 0 \), which simplifies to \( 4 - x = 0 \). This is also a valid step, and meets the condition.
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\( 12 - x = -8 \)
- Subtracting 8 from both sides would lead to \( 12 - x + 8 = 0 \) or \( 20 - x = 0 \). This still works but isn't what we were looking for originally (doesn't involve the positive 8).
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\( 12 = -x - 8 \)
- Subtracting 8 would yield \( 12 + 8 = -x \), or \( 20 = -x \). This is also not the correct origin.
Among these, both options 1 and 2 could lead to a valid step of subtracting \( 8 \) from both sides, but option 1, \( 12 = -x + 8 \), seems to be the equation where subtracting \( 8 \) directly is clear and straightforward.
Therefore, the best option that fits the requirement is:
12 = -x + 8 (option 1).
3 answers