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 = −x + 8

12 − x = 8

12 = −x − 8.

Answer 1

To find the equation that Tillie is solving, we need to analyze how subtracting 8 from both sides affects the equation.

If Tillie subtracts 8 from both sides of the equation, we can represent the original equation as:

\[ A = B \]

After subtracting 8 from both sides, we get:

\[ A - 8 = B - 8 \]

Now let's examine the provided options to see which one can lead to a scenario where subtracting 8 allows for x to be solved:

1. **12 − x = −8**
If we subtract 8 from both sides, we get:
\[ 12 - x - 8 = -8 - 8 \]
which simplifies to:
\[ 4 - x = -16 \]

2. **12 = −x + 8**
If we subtract 8 from both sides, we get:
\[ 12 - 8 = -x + 8 - 8 \]
which simplifies to:
\[ 4 = -x \]

3. **12 − x = 8**
If we subtract 8 from both sides, we get:
\[ 12 - x - 8 = 8 - 8 \]
which simplifies to:
\[ 4 - x = 0 \]
(This could also lead to solving \( x = 4 \).)

4. **12 = −x − 8**
If we subtract 8 from both sides, we get:
\[ 12 - 8 = -x - 8 - 8 \]
which simplifies to:
\[ 4 = -x - 16 \]

The equation that Tillie could be solving that allows her to apply the step of subtracting 8 from both sides and continues the solution process smoothly is:

**12 = −x + 8.**

Thus, the answer is **12 = −x + 8.**