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.