The inequality is:

$3y + 8 \geq 23$

Step-by-Step Solution:

1. Isolate the term with $y$: Subtract 8 from both sides: $3y \geq 23 - 8$ $3y \geq 15$

2. Solve for $y$: Divide both sides by 3: $y \geq \frac{15}{3}$ $y \geq 5$

Final Solution:

$y \geq 5$

This means $y$ must be greater than or equal to 5.

Would you like a graph of the solution or a deeper explanation?

Here are some follow-up questions for practice:

1. What would the solution look like if the inequality were $3y + 8 \leq 23$?
2. How do we solve inequalities when multiplying or dividing by a negative number?
3. Can you write another inequality with a solution of $y \geq 5$?
4. How does solving an equation differ from solving an inequality?
5. What is the meaning of the solution $y \geq 5$ in a real-world context?

Tip: Always reverse the inequality symbol when multiplying or dividing both sides by a negative number!