To solve the inequality:

$12x + 31 \leq 5$

Step-by-Step Solution:

1. Isolate the term with $x$: Subtract 31 from both sides:

   $12x \leq 5 - 31$

   Simplify the right side:

   $12x \leq -26$

2. Solve for $x$: Divide both sides by 12:

   $x \leq \frac{-26}{12}$

   Simplify the fraction:

   $x \leq -\frac{13}{6}$

Final Answer:

The solution to the inequality is:

$x \leq -\frac{13}{6}$

Additional Questions:

1. What is the decimal representation of $-\frac{13}{6}$?
2. How would the solution change if the inequality were $12x + 31 > 5$?
3. How do you graph the solution set $x \leq -\frac{13}{6}$ on a number line?
4. What are the possible integer values of $x$ that satisfy the inequality?
5. How would you solve the inequality if it were $12x + 31 \geq 5$?

Tip:

When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number!