Question

Ava used the following equation in order to solve a math problem involving integers.

−
h
−
k
=
j
If the equation Ava used is correct, which of the following equations must also be correct?

Select all that apply.

Responses

−
j
=
h
−
k
negative j is equal to h over negative k

−
j
=
−
h
k
negative j is equal to negative h over k

j
=
h
k
j is equal to h over k

−
j
=
−
h
−
k

Answer 1

Given the equation:

\[
-h - k = j
\]

We can manipulate this equation to find out which of the provided equations must also be correct.

1. Start with the original equation:
\[
-h - k = j
\]

2. We can isolate \( j \) by multiplying the entire equation by -1:
\[
h + k = -j
\]

This is equivalent to:
\[
-j = h + k
\]

### Analyzing the proposed answers:

1. **−j = h − k**:
- This is *not* correct since we found \( -j = h + k \), not \( h - k \).

2. **−j = −h k**:
- This is *not* correct because it does not correspond to the derived equation.

3. **j = hk**:
- This is also *not* correct. We do not have a relation that corresponds to \( j \) being equal to \( h \) over \( k \).

4. **−j = −h − k**:
- Rearranging the equation gives us \( -j = -(h + k) \). This simplifies to \( -j = -h - k \), which is equivalent to our derived form.

### Conclusion:
The only correct equation from the given responses is:

- **−j = −h − k**.

So, the correct response is:

**−j = −h − k**.