Question

graph each compound inequality.

1. ( x > - 3 ) and ( x leq 1 )
2. ( x > 4 ) or ( x < - 2 )
3. ( 0 leq x leq 5 )

Explanation:

for 27:

Step1: Identify the interval

The compound inequality \(x > -3\) and \(x \leq 1\) means all numbers between -3 and 1, not including -3 (open circle) and including 1 (closed circle).

for 28:

Step1: Identify the intervals

The compound inequality \(x > 4\) or \(x < -2\) means two separate intervals: numbers greater than 4 (open circle at 4, arrow right) and numbers less than -2 (open circle at -2, arrow left).

for 29:

Step1: Identify the interval

The compound inequality \(0 \leq x \leq 5\) means all numbers between 0 and 5, including both 0 and 5 (closed circles at both ends).

Answer:

1. A line segment from an open circle at -3 to a closed circle at 1.
2. An open circle at -2 with an arrow left, and an open circle at 4 with an arrow right.
3. A line segment from a closed circle at 0 to a closed circle at 5.