Question

1. what is the correct graph for the inequality $3 \geq x$?

a. open circle at 3 with shading to the right
b. open circle at 3 with shading to the left
c. closed circle at 3 with shading to the left
d. closed circle at 3 with shading to the right

Explanation:

Step1: Analyze inequality symbol

The inequality is $3 \geq x$ (or $x \leq 3$). The $\geq$ symbol means "greater than or equal to", so 3 is included.

Step2: Determine circle type

Included values use closed circles. So mark 3 with a closed circle.

Step3: Determine shading direction

$x \leq 3$ means x values less than or equal to 3. On a number line, these are to the left of 3. Shade left.

Step4: Match with options

Closed circle at 3 + shading left corresponds to option c.

Answer:

c. Closed circle at 3 with shading to the left