Solve for p.
–
17p–14≥
–
19p+4 or 
–
6p+17+15p≤17
Write your answer as a compound inequality with integers

Let's solve the inequalities step by step:

### First inequality: 
\[
17p - 14 \geq 19p + 4
\]
1. Subtract \(19p\) from both sides:
\[
17p - 19p - 14 \geq 4
\]
This simplifies to:
\[
-2p - 14 \geq 4
\]
2. Add 14 to both sides:
\[
-2p \geq 18
\]
3. Divide both sides by \(-2\) (remember to reverse the inequality sign when dividing by a negative number):
\[
p \leq -9
\]

### Second inequality:
\[
6p + 17 + 15p \leq 17
\]
1. Combine like terms:
\[
(6p + 15p) + 17 \leq 17
\]
This simplifies to:
\[
21p + 17 \leq 17
\]
2. Subtract 17 from both sides:
\[
21p \leq 0
\]
3. Divide both sides by 21:
\[
p \leq 0
\]

### Final Solution:
We now have two inequalities:
1. \(p \leq -9\)
2. \(p \leq 0\)

The solution to this compound inequality is:
\[
p \leq -9 \quad \text{or} \quad p \leq 0
\]

Since the first inequality is more restrictive (\(p \leq -9\)), the final solution is:
\[
p \leq -9
\]

Would you like further details on any step or have any other questions?

Here are 5 related questions for further exploration:
1. How do we handle inequalities when dividing by a negative number?
2. What are the rules for solving compound inequalities?
3. Can you graph the solution on a number line?
4. How do you solve a system of inequalities?
5. What happens if the solution is a range rather than a single condition?

**Tip:** Always be cautious of flipping the inequality sign when multiplying or dividing by a negative number.

Solve for p. 17p - 14 ≥ 19p + 4 or 6p + 17 + 15p ≤ 17. Write your answer as a compound inequality with integers.

Learn how to solve the compound inequality 17p - 14 ≥ 19p + 4 or 6p + 17 + 15p ≤ 17 with step-by-step explanations. This algebra problem covers key concepts like solving inequalities and handling compound inequalities. Suitable for students in Grades 9-11.

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