1. The problem states: "-5 increased by one-half of a number is a maximum of 3." We need to express this as an inequality. 2. Let the number be represented by $x$. 3. "-5 increased by one-half of a number" translates to $$-5 + \frac{1}{2}x$$. 4. "is a maximum of 3" means the expression is less than or equal to 3, so we write: $$-5 + \frac{1}{2}x \leq 3$$ 5. To isolate $x$, add 5 to both sides: $$\frac{1}{2}x \leq 3 + 5$$ $$\frac{1}{2}x \leq 8$$ 6. Multiply both sides by 2 to solve for $x$: $$x \leq 16$$ 7. Therefore, the inequality is: $$x \leq 16$$ This means the number $x$ can be any value less than or equal to 16.