Question

linear inequalities graphing a linear inequality on the number line graph the inequality below on the number line. a > 5

Explanation:

Step1: Identify the critical point

The inequality is \(a > 5\), so the critical value is \(5\).

Step2: Determine the type of circle

Since the inequality is \(>\) (not \(\geq\)), we use an open circle at \(5\) to show that \(5\) is not included in the solution set.

Step3: Determine the direction of the line

For \(a > 5\), the solutions are all numbers greater than \(5\), so we draw an arrow starting from the open circle at \(5\) and pointing to the right (towards positive infinity).

To graph it on the given number line:

1. Locate \(5\) on the number line.
2. Draw an open circle at \(5\) (because \(a\) is strictly greater than \(5\), not equal to \(5\)).
3. Draw a line (or arrow) starting from the open circle at \(5\) and extending to the right (towards \(6, 7, 8, \dots\)) to represent all numbers greater than \(5\).

Answer:

To graph \(a > 5\) on the number line:

• Place an open circle at \(5\) (since \(5\) is not included in the solution as the inequality is \(>\), not \(\geq\)).
• Draw an arrow starting from the open circle at \(5\) and pointing to the right (towards values like \(6, 7, 8, \dots\)) to show all numbers greater than \(5\) are part of the solution set.