Question

directions: graph each inequality on the number line. 1. x > - 2 2. x ≤ 5 3. x ≥ 1 4. 3 < x

Explanation:

Step1: Identify inequality type for \(x > - 2\)

For \(x > - 2\), we use an open - circle at \(-2\) (since \(x\) is not equal to \(-2\)) and draw an arrow to the right on the number line.

Step2: Identify inequality type for \(x\leq5\)

For \(x\leq5\), we use a closed - circle at \(5\) (since \(x\) can be equal to \(5\)) and draw an arrow to the left on the number line.

Step3: Identify inequality type for \(x\geq1\)

For \(x\geq1\), we use a closed - circle at \(1\) (since \(x\) can be equal to \(1\)) and draw an arrow to the right on the number line.

Step4: Identify inequality type for \(3 < x\) (same as \(x>3\))

For \(x > 3\), we use an open - circle at \(3\) (since \(x\) is not equal to \(3\)) and draw an arrow to the right on the number line.

Answer:

1. For \(x > - 2\): Open - circle at \(-2\), arrow to the right.
2. For \(x\leq5\): Closed - circle at \(5\), arrow to the left.
3. For \(x\geq1\): Closed - circle at \(1\), arrow to the right.
4. For \(3 < x\): Open - circle at \(3\), arrow to the right.