Question

1. which inequality is represented by a closed circle at 5 and shading to the right on a number line?

a. ( x > 5 )
b. ( x leq 5 )
c. ( x geq 5 )
d. ( x < 5 )

Explanation:

Step1: Recall the rules of number - line representation for inequalities

A closed circle on a number line means the number is included in the solution set. Shading to the right means the values are greater than or equal to the number.

Step2: Analyze each option

• Option a: \(x>5\) has an open circle at \(5\) (since \(5\) is not included).
• Option b: \(x\leq5\) has a closed circle at \(5\) but shades to the left.
• Option c: \(x\geq5\) has a closed circle at \(5\) (because \(5\) is included) and shades to the right.
• Option d: \(x < 5\) has an open circle at \(5\) and shades to the left.

Answer:

C. \(x\geq5\)