Question

graph the compound inequality on the number line. ( x > 0 ) and ( x < 3 )

Explanation:

Step1: Analyze the compound inequality

The compound inequality is \(x > 0\) and \(x < 3\), which can be written as \(0 < x < 3\). This means we are looking for all real numbers \(x\) that are greater than \(0\) and less than \(3\).

Step2: Determine the endpoints on the number line

• For \(x > 0\), we use an open circle at \(0\) because \(x\) is not equal to \(0\).
• For \(x < 3\), we use an open circle at \(3\) because \(x\) is not equal to \(3\).

Step3: Shade the region between the endpoints

We shade the region on the number line that is between \(0\) and \(3\) (excluding the endpoints themselves) to represent all the values of \(x\) that satisfy both inequalities.

Answer:

To graph \(0 < x < 3\) on the number line:

1. Place an open circle at \(0\) (since \(x

eq0\)).

1. Place an open circle at \(3\) (since \(x

eq3\)).

1. Shade the line segment between the open circle at \(0\) and the open circle at \(3\).