https://file.aiquickdraw.com/mathbot/file/1726807504611vht61uh3.jpg

The inequality you provided from the image is:

\[
-14 \leq w + 30 \leq 3w - 27
\]

This is a compound inequality. To solve it, we will break it down into two parts:

1. \(-14 \leq w + 30\)
2. \(w + 30 \leq 3w - 27\)

### Solving Part 1: \(-14 \leq w + 30\)

Subtract 30 from both sides:

\[
-14 - 30 \leq w
\]
\[
-44 \leq w
\]

Thus, \(w \geq -44\).

### Solving Part 2: \(w + 30 \leq 3w - 27\)

Subtract \(w\) from both sides:

\[
30 \leq 2w - 27
\]

Add 27 to both sides:

\[
57 \leq 2w
\]

Divide by 2:

\[
w \geq 28.5
\]

### Combining the Results

From Part 1, we have \(w \geq -44\).  
From Part 2, we have \(w \geq 28.5\).

Thus, the solution for \(w\) is \(w \geq 28.5\), because \(w \geq -44\) is less restrictive than \(w \geq 28.5\).

### Final Answer:

\[
w \geq 28.5
\]

Let me know if you need more details or have any questions! 

Here are 5 related questions to expand on this:

1. How do we solve inequalities involving fractions?
2. What happens if the inequality signs are reversed?
3. How do you solve a compound inequality involving an absolute value?
4. Can inequalities have no solution? How can that happen?
5. How does the solution change if we divide or multiply by a negative number?

**Tip**: When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign!

Learn how to solve the compound inequality -14 ≤ w + 30 ≤ 3w - 27 with a step-by-step breakdown. This problem involves algebraic manipulation of inequalities and is suitable for students in Grades 8-10.

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