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The given problem is:

\[
5p + 3 \geq 38
\]

Let's solve it step by step:

1. **Subtract 3 from both sides** to isolate the term with \( p \):

\[
5p \geq 38 - 3
\]

\[
5p \geq 35
\]

2. **Divide both sides by 5** to solve for \( p \):

\[
p \geq \frac{35}{5}
\]

\[
p \geq 7
\]

So, the solution is \( p \geq 7 \).

Would you like more details or have any questions?

Here are 5 related questions you might consider:

1. What happens if the inequality sign was reversed (e.g., \( 5p + 3 \leq 38 \))?
2. How would the solution change if there was a negative coefficient for \( p \)?
3. Can you graph the solution \( p \geq 7 \) on a number line?
4. What if the inequality had an equal sign, \( 5p + 3 = 38 \)? What would the solution be?
5. How do inequalities differ from equations in terms of solving them?

**Tip**: When multiplying or dividing both sides of an inequality by a negative number, remember to flip the inequality sign!

Learn how to solve the inequality 5p + 3 ≥ 38 with a detailed, step-by-step algebraic solution. This problem demonstrates core algebraic concepts and theorems including basic inequality manipulation, addition property of inequality, and solving linear inequalities. Ideal for Grades 9-10 students.

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