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The inequality to solve is:

\[
|5t - 6| \leq 4
\]

### Step 1: Break the absolute value inequality into two cases.

By definition of absolute value, the inequality \( |A| \leq B \) translates into:

\[
-B \leq A \leq B
\]

In this case, the expression inside the absolute value is \( 5t - 6 \), and \( B = 4 \). So, the inequality becomes:

\[
-4 \leq 5t - 6 \leq 4
\]

### Step 2: Solve the compound inequality.

First, solve the left side:

\[
-4 \leq 5t - 6
\]

Add 6 to both sides:

\[
2 \leq 5t
\]

Now, divide by 5:

\[
\frac{2}{5} \leq t
\]

Next, solve the right side:

\[
5t - 6 \leq 4
\]

Add 6 to both sides:

\[
5t \leq 10
\]

Now, divide by 5:

\[
t \leq 2
\]

### Step 3: Combine the solutions.

The solution set is:

\[
\frac{2}{5} \leq t \leq 2
\]

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

In interval notation, the solution is:

\[
\left[ \frac{2}{5}, 2 \right]
\]

Therefore, the correct choice is **A**, with the solution set being \( \left[ \frac{2}{5}, 2 \right] \).

Would you like more details or have any questions?

Here are 5 related questions to further explore:
1. How would the solution change if the inequality was \( |5t - 6| > 4 \)?
2. How can you graph this solution set on a number line?
3. What is the meaning of "absolute value" geometrically?
4. How would you solve \( |5t - 6| \geq 4 \) as a compound inequality?
5. Can you generalize the process for any inequality involving absolute values?

**Tip:** Always double-check your compound inequality by solving both sides separately before combining the results.

Solve the following inequality: |5t - 6| ≤ 4. Graph the solution set.

Learn how to solve the absolute value inequality |5t - 6| ≤ 4 with a step-by-step solution, breaking it down into a compound inequality. The final solution is given in interval notation. Suitable for students in Grades 9-11.

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