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The problem asks to translate the given condition into an inequality and solve for \( m \).

### Problem Breakdown:
- We are told that 16 is subtracted from half of the number \( m \).
- The result of this subtraction is at most 28, which means the result can be 28 or less.

### Step 1: Set up the inequality
Let’s denote the number by \( m \). 
- Half of \( m \) is written as \( \frac{m}{2} \).
- The phrase "16 is subtracted from half of the number \( m \)" means \( \frac{m}{2} - 16 \).
- The phrase "the result is at most 28" means \( \frac{m}{2} - 16 \leq 28 \).

So the inequality is:
\[
\frac{m}{2} - 16 \leq 28
\]

### Step 2: Solve the inequality
1. Add 16 to both sides to isolate the \( \frac{m}{2} \) term:
\[
\frac{m}{2} \leq 28 + 16
\]
\[
\frac{m}{2} \leq 44
\]

2. Multiply both sides by 2 to solve for \( m \):
\[
m \leq 44 \times 2
\]
\[
m \leq 88
\]

### Conclusion:
The possible values of \( m \) are all numbers such that \( m \leq 88 \). In other words, \( m \) must be less than or equal to 88.

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Would you like any further explanation or details?

Here are some related questions for further exploration:
1. What happens if the inequality is "greater than or equal to" instead?
2. How would you solve the problem if the subtraction was reversed?
3. Can you graph this inequality on a number line?
4. How would the solution change if the result was "exactly 28" instead of "at most 28"?
5. How would this change if the number subtracted was different, say 10 instead of 16?

**Tip**: When solving inequalities, make sure to reverse the inequality sign if you multiply or divide by a negative number!

When 16 is subtracted from half of the number m, the result is at most 28. Write this as an inequality and solve to find the possible values of m.

Learn how to solve the inequality where 16 is subtracted from half of a number, and the result is at most 28. This problem focuses on algebraic manipulation and solving inequalities, suitable for students in Grades 6-8.

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