Question

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

Explanation:

Step1: Convert mixed number to fraction

$2\frac{1}{2} = \frac{5}{2}$, so inequality becomes:
$\frac{1}{3}c - \frac{5}{2} \geq \frac{1}{2}$

Step2: Add $\frac{5}{2}$ to both sides

$\frac{1}{3}c - \frac{5}{2} + \frac{5}{2} \geq \frac{1}{2} + \frac{5}{2}$
$\frac{1}{3}c \geq \frac{6}{2}$
$\frac{1}{3}c \geq 3$

Step3: Multiply by 3 on both sides

$\frac{1}{3}c \times 3 \geq 3 \times 3$
$c \geq 9$

Step4: Graph on number line

Draw a closed dot at 9, shade all values to the right of 9 on the number line.

Answer:

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