Question

part 4 of 5 (c) the solution set in interval notation for |h - 1| < 6 is (-5, 7). part: 4 / 5 part 5 of 5 graph the solution set for |h - 1| < 6.

Explanation:

Step1: Recall the solution interval

From part (c), the solution to \(|h - 1| < 6\) is \((-5, 7)\). This means \(h\) is greater than \(-5\) and less than \(7\).

Step2: Determine the graph elements

• For an open interval \((a, b)\), we use open circles (since the endpoints are not included) at \(a\) and \(b\), and a line segment connecting them to represent all the values in between.
• Here, \(a=-5\) and \(b = 7\). So we place an open circle at \(-5\) and an open circle at \(7\), then draw a line between them on the number line.

Answer:

To graph the solution set \((-5, 7)\) for \(|h - 1| < 6\):

1. Locate \(-5\) and \(7\) on the number line.
2. Place an open circle (○) at \(-5\) (because \(-5\) is not included in the solution, as the interval is open) and an open circle (○) at \(7\) (for the same reason).
3. Draw a line segment connecting the two open circles to represent all the values of \(h\) between \(-5\) and \(7\).