Question

solve the inequality and graph the solution.

z - 1 > 3

plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

submit

Explanation:

Step1: Isolate the variable \( z \)

Add \( 1 \) to both sides of the inequality \( z - 1>3 \).
Using the addition property of inequalities \( z-1 + 1>3 + 1 \).

Step2: Simplify

Simplify the left - hand side \( z-1 + 1=z \) and the right - hand side \( 3 + 1 = 4 \). So, \( z>4 \).

To graph \( z>4 \):

• The endpoint is \( z = 4 \). Since the inequality is strict (\(>\)), we use an open circle at \( z = 4 \).
• The solution set is all real numbers greater than \( 4 \), so we draw a ray starting at the open circle at \( 4 \) and extending to the right.

Answer:

The solution of the inequality \( z-1>3 \) is \( z>4 \). On the number line, we have an open circle at \( 4 \) and a ray extending to the right.