To determine which equation Tille is solving by subtracting 8 from both sides, we can analyze each option:
-
12 - x = -8
- If Tille subtracts 8 from both sides: \[ 12 - x - 8 = -8 - 8 \] This simplifies to: \[ 4 - x = -16 \]
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12 - x = 8
- If Tille subtracts 8 from both sides: \[ 12 - x - 8 = 8 - 8 \] This simplifies to: \[ 4 - x = 0 \] or \[ 12 - x - 8 = 0 \]
-
12 = -x - 8
- If Tille subtracts 8 from both sides: \[ 12 - 8 = -x - 8 \] This simplifies to: \[ 4 = -x - 8 \]
-
12 = -x + 8
- If Tille subtracts 8 from both sides: \[ 12 - 8 = -x + 8 \] This simplifies to: \[ 4 = -x + 8 \]
Now, Note that the first equation \(12 - x = -8\) yields \(4 - x = -16\) after Tille's operation. However, it can be inferred that the most likely equation where subtracting 8 would immediately yield an equation is 12 - x = 8 as it directly becomes 4 - x = 0 after subtracting 8, simplifying either to \(x = 4\) or confirming \(- x = -4\) implying that she might be trying to balance them positively without complications.
The conclusion is that the equation Tille is most likely trying to solve is:
12 - x = 8.