Sure! Let's break down the problem step by step.
### Step 1: Understanding the Statement
The problem states that when 16 is subtracted from half of a number [tex]\( m \)[/tex], the result is at most 28.
### Step 2: Formulating the Inequality
We can translate the given condition into a mathematical expression. Let’s break down the statement:
1. Half of the number [tex]\( m \)[/tex]: [tex]\(\frac{m}{2}\)[/tex].
2. Subtracted by 16: [tex]\(\frac{m}{2} - 16\)[/tex].
3. The result is at most 28: This means the result is less than or equal to 28, which can be written as [tex]\(\leq 28\)[/tex].
Combining these, we get the inequality:
[tex]\[
\frac{m}{2} - 16 \leq 28
\][/tex]
### Step 3: Solving the Inequality
To find the possible values of [tex]\( m \)[/tex], we need to solve this inequality step by step.
1. Start with the inequality:
[tex]\[
\frac{m}{2} - 16 \leq 28
\][/tex]
2. Add 16 to both sides to isolate the term with [tex]\( m \)[/tex] on one side:
[tex]\[
\frac{m}{2} - 16 + 16 \leq 28 + 16
\][/tex]
[tex]\[
\frac{m}{2} \leq 44
\][/tex]
3. Next, we need to get rid of the fraction by multiplying both sides by 2:
[tex]\[
2 \left(\frac{m}{2}\right) \leq 44 \cdot 2
\][/tex]
[tex]\[
m \leq 88
\][/tex]
### Conclusion
The possible values of [tex]\( m \)[/tex] that satisfy the given condition are:
[tex]\[
m \leq 88
\][/tex]
Thus, the inequality [tex]\( m \leq 88 \)[/tex] represents the solution to the problem.
