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

Question

−
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.