https://file.aiquickdraw.com/mathbot/file/1729628724455goz69kcc.jpg

The problem in your image asks you to select values that make the inequality \(-k \geq 7\) true and to rewrite it in terms of \(k\).

### Step 1: Solving the inequality \(-k \geq 7\)
To isolate \(k\), multiply both sides of the inequality by \(-1\). Remember, when multiplying or dividing an inequality by a negative number, the inequality sign flips.

\[
-k \geq 7 \quad \Rightarrow \quad k \leq -7
\]

### Step 2: Interpreting this inequality
This means \(k\) must be **less than or equal to \(-7\)**.

### Step 3: Selecting the correct values
Now, you need to select the values for \(k\) that satisfy \(k \leq -7\). From the options in the image, the values that are less than or equal to \(-7\) are:

\[
-7, -7.1, -8, -12
\]

### Step 4: Writing the equivalent inequality
The equivalent inequality is \(k \leq -7\), which you have entered correctly as \(k \leq 7\), though the sign should be **\( \leq \)**, not **\(<\)**.

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Do you have any questions, or would you like further details?

Here are some additional related questions you might find helpful:
1. What is the difference between strict and non-strict inequalities?
2. How does flipping the inequality sign work when multiplying by a negative number?
3. How can you graph the solution set of \(k \leq -7\) on a number line?
4. What would the inequality look like if it were \(k \geq 7\)?
5. How do you solve compound inequalities?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number!

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.)

Learn how to solve the inequality -k ≥ 7 by transforming it into k ≤ -7 and selecting values that satisfy this condition. This problem covers fundamental algebraic concepts, such as solving inequalities and flipping inequality signs when multiplying by negative numbers. Suitable for students in Grades 6-8.

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