Tillie is solving an equation for x

Question

. 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 minus x equals negative 8

12 − x = 8
12 minus x equals 8

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

12 = −x − 8

Answer 1

To determine which equation Tillie is solving by subtracting 8 from both sides, we can analyze the original equations and see which one allows for that operation to make sense.

1. 12 − x = −8
   Subtracting 8 from both sides:
   \( 12 - x - 8 = -8 - 8 \)
   \( 4 - x = -16 \) (This is valid.)

2. 12 − x = 8
   Subtracting 8 from both sides:
   \( 12 - x - 8 = 8 - 8 \)
   \( 4 - x = 0 \) (This is valid.)

3. 12 = −x + 8
   Subtracting 8 from both sides:
   \( 12 - 8 = -x + 8 - 8 \)
   \( 4 = -x \) (This is valid.)

4. 12 = −x − 8
   Subtracting 8 from both sides:
   \( 12 - 8 = -x - 8 - 8 \)
   \( 4 = -x - 16 \) (This is valid.)

However, we need to check which equation, after the subtracting step, leads to a simpler form or a proper equation to solve for \( x \).

The first equation simplifies correctly but does not produce a straightforward equation for \( x \). The second equation straightforwardly yields \( x = 4 \). The third equation yields \( x = -4 \). The fourth will require more manipulation.

Given that we know subtracting 8 does make sense for the second equation, the most straightforward equation Tillie is likely solving is:

12 − x = 8 (the answer is: 12 minus x equals 8).