https://file.aiquickdraw.com/mathbot/file/1727320123201uu0z06qz.jpg

The inequality in the image is:

\[
-12 \leq 2k - 10 \leq -6
\]

This is a compound inequality, which we can solve by isolating \( k \).

### Step-by-step solution:

1. **Add 10 to all parts of the inequality:**
   \[
   -12 + 10 \leq 2k - 10 + 10 \leq -6 + 10
   \]
   Simplifying this gives:
   \[
   -2 \leq 2k \leq 4
   \]

2. **Divide through by 2:**
   \[
   \frac{-2}{2} \leq \frac{2k}{2} \leq \frac{4}{2}
   \]
   Simplifying this gives:
   \[
   -1 \leq k \leq 2
   \]

### Final solution:
\[
-1 \leq k \leq 2
\]

So, the solution for \( k \) is the interval \( [-1, 2] \).

Would you like further explanation, or do you have any questions about the solution?

Here are five related questions to explore further:

1. How do you solve inequalities involving variables on both sides?
2. What is the difference between solving a single inequality and a compound inequality?
3. How would the solution change if we multiplied or divided the inequality by a negative number?
4. What is the graphical representation of the solution on a number line?
5. How can we apply compound inequalities in real-life situations?

**Tip:** Always be careful when dividing or multiplying inequalities by negative numbers; the inequality sign flips direction.

This page explains how to solve the compound inequality -12 ≤ 2k - 10 ≤ -6 step by step. Learn key algebra concepts such as solving inequalities by adding and dividing constants. Suitable for students in Grades 7-9.

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