https://file.aiquickdraw.com/mathbot/file/1726434578831asw3a9o4.jpg

The inequality provided in the image is:

\[
|3p - 2| - 3 \leq 7
\]

Let's solve it step by step:

### Step 1: Isolate the absolute value
First, add 3 to both sides of the inequality to isolate the absolute value term:

\[
|3p - 2| \leq 7 + 3
\]
\[
|3p - 2| \leq 10
\]

### Step 2: Break into two inequalities
For absolute value inequalities, we remove the absolute value and create a compound inequality:

\[
-10 \leq 3p - 2 \leq 10
\]

### Step 3: Solve the compound inequality
Now, solve this compound inequality by isolating \( p \).

1. Add 2 to all parts of the inequality:
   \[
   -10 + 2 \leq 3p \leq 10 + 2
   \]
   \[
   -8 \leq 3p \leq 12
   \]

2. Divide all parts by 3 to solve for \( p \):
   \[
   \frac{-8}{3} \leq p \leq \frac{12}{3}
   \]
   \[
   -\frac{8}{3} \leq p \leq 4
   \]

### Final Answer:
The solution as a compound inequality is:
\[
-\frac{8}{3} \leq p \leq 4
\]

Would you like further details on this solution or another clarification?

### Related Questions:
1. How do you solve inequalities with absolute values?
2. What is the difference between "and" and "or" compound inequalities?
3. Can absolute value inequalities have no solution?
4. How do you graph the solution to a compound inequality on a number line?
5. How does multiplying or dividing by a negative number affect an inequality?

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

Solve the inequality |3p - 2| - 3 ≤ 7. Submit your answer as a compound inequality.

Learn how to solve the absolute value inequality |3p - 2| - 3 ≤ 7 with a step-by-step breakdown. This problem uses key algebraic concepts such as absolute value inequalities and compound inequalities. Ideal for students in Grades 8-10.

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