Question

Question
Tillie is solving an equation for x
. Her first step is to subtract 8 from both sides of the equation. Which equation is she solving?(1 point)
Responses

12 = −x − 8
12 equals negative x minus 8

12 − x = −8
12 minus x equals negative 8

12 = −x + 8
12 equals negative x plus 8

12 − x = 8

Answer 1

To determine which equation Tillie is solving, we need to analyze the effect of subtracting 8 from both sides.

If she subtracts 8 from both sides, then we can represent this mathematically:

1. Let's take each of the given equations and imagine subtracting 8 from both sides.

For the first equation:
- \( 12 = -x - 8 \)
Subtracting 8 from both sides gives:
\( 12 - 8 = -x - 8 \) → \( 4 = -x \) (valid)

For the second equation:
- \( 12 - x = -8 \)
Subtracting 8 from both sides gives:
\( 12 - x - 8 = -8 \) → \( 4 - x = -8 \) (valid)

For the third equation:
- \( 12 = -x + 8 \)
Subtracting 8 from both sides gives:
\( 12 - 8 = -x + 8 \) → \( 4 = -x + 8 \) (valid)

For the fourth equation:
- \( 12 - x = 8 \)
Subtracting 8 from both sides gives:
\( 12 - x - 8 = 8 \) → \( 4 - x = 0 \) (valid)

Next, let’s reframe the origin statement. We need to identify an equation such that when 8 is subtracted from it, we will still have a valid, logical expression.

Looking at the equations, the most straightforward equation from which subtracting 8 leads directly to a simpler form is the fourth equation:
- From \( 12 - x = 8 \), when we subtract 8 from both sides, we successfully arrive at \( 12 - x - 8 = 0 \).

Thus, the equation Tillie is likely solving is:

**12 − x = 8**