Question

what does a closed circle on a number line indicate when graphing an inequality?
a. the variable is equal to or greater/less than the value
b. the inequality cannot be solved
c. the variable is strictly greater than the value
d. the variable is strictly less than the value

Explanation:

When graphing inequalities on a number line, a closed circle is used to show that the number it is placed on is included in the solution set. This means the variable can be equal to that number (along with being greater or less than, depending on the inequality sign). For example, in \(x\geq a\) or \(x\leq a\), we use a closed - circle at \(x = a\).

• Option b is incorrect because a closed circle has nothing to do with the solvability of the inequality. All simple linear inequalities of the form \(ax + b>c\), \(ax + b\geq c\), \(ax + b < c\), \(ax + b\leq c\) (where \(a

eq0\)) are solvable.

• Option c (\(x>a\)) and option d (\(x < a\)) use an open circle. An open circle is for strict inequalities (\(>\) or \(<\)) where the number on the number - line is not included in the solution set.

Answer:

A. The variable is equal to or greater/less than the value