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Let's break down the problem:

We are given the statement:

"When 14 is subtracted from half of the number \( k \), the result is at most 18."

### Step 1: Convert the sentence into an inequality.

1. "Half of the number \( k \)" can be expressed as \( \frac{k}{2} \).
2. Subtracting 14 from this: \( \frac{k}{2} - 14 \).
3. The result is "at most 18," which means it is less than or equal to 18. So, we write:
   \[
   \frac{k}{2} - 14 \leq 18
   \]

### Step 2: Solve the inequality.

1. Start with:
   \[
   \frac{k}{2} - 14 \leq 18
   \]

2. Add 14 to both sides:
   \[
   \frac{k}{2} \leq 32
   \]

3. Multiply both sides by 2 to get rid of the fraction:
   \[
   k \leq 64
   \]

### Final answer:
The possible values of \( k \) are \( k \leq 64 \).

Would you like more details on any step or have questions?

Here are 5 questions that expand on this:

1. What is the difference between "at most" and "less than" in inequalities?
2. How do you solve inequalities involving fractions?
3. What happens if the inequality used the phrase "at least" instead?
4. Could this inequality be written in a different form? Why or why not?
5. How does adding or subtracting values affect inequalities?

**Tip:** Always remember that when you multiply or divide both sides of an inequality by a negative number, you need to reverse the inequality symbol!

When 14 is subtracted from half of the number k, the result is at most 18. Write this as an inequality and solve to find the possible values of k.

Learn how to write and solve an inequality where 14 is subtracted from half of the number k, and the result is at most 18. This algebra problem introduces key concepts in inequalities and solving linear equations, suitable for Grades 7-9.

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