Question: Select the values that make the inequality $-k < 7$ true.
Then write an equivalent inequality, in terms of $k$.
(Numbers written in order from least to greatest going across.)
1. **State the problem:** We want to find all values of $k$ such that the inequality $-k < 7$ holds true.
2. **Rewrite the inequality:** Starting with
$$-k < 7$$
we want to isolate $k$. To do this, multiply both sides by $-1$. Remember, multiplying or dividing an inequality by a negative number reverses the inequality sign.
3. **Multiply both sides by $-1$ and reverse the inequality:**
$$\cancel{-1} \times (-k) > \cancel{-1} \times 7$$
which simplifies to
$$k > -7$$
4. **Interpret the inequality:** The values of $k$ that satisfy $k > -7$ are all numbers greater than $-7$.
5. **Select values from the given list:** The numbers greater than $-7$ from the list are:
$$-6.9, -6, -2, 0, 2, 6, 6.9, 7, 7.1, 8, 12$$
6. **Final answer:**
- Values that make $-k < 7$ true are:
$$-6.9, -6, -2, 0, 2, 6, 6.9, 7, 7.1, 8, 12$$
- Equivalent inequality in terms of $k$ is:
$$k > -7$$