https://file.aiquickdraw.com/mathbot/file/17267203268145liyfwrw.jpg

The inequality in the image is:

\[
-5 \leq \frac{6x - 5}{2} \leq 4
\]

Let's solve this step by step.

### Step 1: Break the inequality into two parts:
\[
-5 \leq \frac{6x - 5}{2}
\]
and
\[
\frac{6x - 5}{2} \leq 4
\]

### Step 2: Solve each part of the inequality.

#### For \( -5 \leq \frac{6x - 5}{2} \):

1. Multiply both sides by 2 to eliminate the denominator:
\[
-5 \times 2 \leq 6x - 5 \quad \Rightarrow \quad -10 \leq 6x - 5
\]
2. Add 5 to both sides:
\[
-10 + 5 \leq 6x \quad \Rightarrow \quad -5 \leq 6x
\]
3. Divide both sides by 6:
\[
\frac{-5}{6} \leq x
\]
So, \( x \geq \frac{-5}{6} \).

#### For \( \frac{6x - 5}{2} \leq 4 \):

1. Multiply both sides by 2:
\[
6x - 5 \leq 4 \times 2 \quad \Rightarrow \quad 6x - 5 \leq 8
\]
2. Add 5 to both sides:
\[
6x \leq 8 + 5 \quad \Rightarrow \quad 6x \leq 13
\]
3. Divide by 6:
\[
x \leq \frac{13}{6}
\]

### Step 3: Combine the two inequalities.

From both parts, we have:
\[
\frac{-5}{6} \leq x \leq \frac{13}{6}
\]

### Step 4: Write the solution in interval notation.

The solution set is:
\[
\left[ \frac{-5}{6}, \frac{13}{6} \right]
\]

Thus, the correct choice is **A**, with the solution set \( \left[ \frac{-5}{6}, \frac{13}{6} \right] \).

Would you like further details or assistance with any step? Here are five related questions to consider:

1. How do you graph inequalities on a number line?
2. Can you solve compound inequalities with different types of inequalities (e.g., strict vs. non-strict)?
3. What happens when you multiply or divide inequalities by negative numbers?
4. How can inequalities be used to represent real-world problems?
5. What is the difference between set notation and interval notation?

**Tip:** When solving inequalities, always be careful when multiplying or dividing by a negative number—this reverses the inequality sign!

Solve the inequality: -5 ≤ (6x - 5)/2 ≤ 4. Give the solution set in both interval and graph forms.

Learn how to solve the inequality -5 ≤ (6x - 5)/2 ≤ 4 with a step-by-step explanation. This problem involves key algebraic concepts such as solving compound inequalities and expressing solutions in interval notation. Suitable for students in Grades 9-12.

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