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Let's solve the given inequality step by step.

The inequality is:
\[
-5p - 1 + 6p \leq 3
\]

### Step 1: Combine like terms
We can combine the terms involving \( p \):
\[
-5p + 6p - 1 \leq 3
\]
\[
p - 1 \leq 3
\]

### Step 2: Isolate \( p \)
To isolate \( p \), add 1 to both sides of the inequality:
\[
p - 1 + 1 \leq 3 + 1
\]
\[
p \leq 4
\]

### Solution
The inequality simplifies to \( p \leq 4 \).

### Answer Format
Since the solution is asking for \( p \) and you have a choice of inequality symbols (\( \leq, \geq, <, > \)), the correct symbol is \( \leq \).

Thus, the solution is:
\[
p \leq 4
\]

Would you like a deeper explanation, or do you have any further questions?

Here are 5 related questions for practice:
1. Solve the inequality \( 3p + 5 \geq 2p - 1 \).
2. How do you solve \( 7p - 4 < 3p + 8 \)?
3. What is the solution to \( 4 - 2p \geq p + 9 \)?
4. Solve \( 2p + 6 \leq 8p - 4 \).
5. If \( p - 3 > 5 \), what is the value of \( p \)?

**Tip**: When solving inequalities, treat them like equations, but remember to reverse the inequality symbol if you multiply or divide by a negative number!

Learn how to solve the linear inequality -5p - 1 + 6p ≤ 3. This step-by-step solution demonstrates key algebraic concepts such as combining like terms and solving inequalities. Suitable for students in Grades 8-10.

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