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 equals negative x plus 8

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

12 − x = 8
12 minus x equals 8

12 = −x − 8

Answer 1

To determine which equation Tillie is solving, we need to assess how subtracting 8 from both sides affects the equations provided.

When Tillie subtracts 8 from both sides, if the original equation was something like \( a = b \), it would become \( a - 8 = b - 8 \).

Let’s evaluate the given options:

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

2. 12 − x = −8
   If we subtract 8 from both sides:
   \( 12 - x - 8 = -8 \)
   \( 4 - x = -8 \) (Not a valid transformation from the original equation.)

3. 12 − x = 8
   If we subtract 8 from both sides:
   \( 12 - x - 8 = 8 - 8 \)
   \( 4 - x = 0 \) (This is a valid transformation.)

4. 12 = −x − 8
   If we subtract 8 from both sides:
   \( 12 - 8 = -x - 8 \)
   \( 4 = -x - 8 \) (This is a valid transformation.)

The two valid transformations based on the original equations are 1, 3, and 4. However, we need to find the equation that leads to a step where subtracting 8 from both sides is the first logical action.

Upon analyzing, the best candidate for the equation where subtracting 8 leads to a simpler form is 12 = -x + 8. Therefore, Tillie must be solving the equation:

12 = −x + 8.