Question

1. $\frac{1}{3}c - 2\frac{1}{2} geq \frac{1}{2}$

Explanation:

Step1: Rewrite mixed numbers as fractions

First, convert $2\frac{1}{2}$ to an improper fraction: $2\frac{1}{2} = \frac{5}{2}$. The inequality becomes:
$$\frac{1}{3}c - \frac{5}{2} \geq \frac{1}{2}$$

Step2: Isolate the term with $c$

Add $\frac{5}{2}$ to both sides to cancel the constant on the left:
$$\frac{1}{3}c \geq \frac{1}{2} + \frac{5}{2}$$
$$\frac{1}{3}c \geq \frac{6}{2}$$
$$\frac{1}{3}c \geq 3$$

Step3: Solve for $c$

Multiply both sides by 3 to isolate $c$:
$$c \geq 3 \times 3$$
$$c \geq 9$$

Step4: Graph the solution

On a number line, draw a closed circle at 9 (since the inequality is $\geq$, including 9) and shade all values to the right of 9.

Answer:

$c \geq 9$
(Graph: Closed circle at 9, shading to the right on the number line)