Solve the inequality and graph the solution.

Question

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.

Answer 1

To solve the inequality \( z - 1 \leq 3 \), we first isolate \( z \):

1. Add 1 to both sides: \[ z - 1 + 1 \leq 3 + 1 \] \[ z \leq 4 \]

So, the solution to the inequality is \( z \leq 4 \).

Graphing the Solution

1. Endpoints:

   • The endpoint of the inequality is \( z = 4 \).
   • Since the inequality is less than or equal to (≤), we will use a closed dot on the number 4 to indicate that it is included in the solution.

2. Direction:

   • The inequality \( z \leq 4 \) means that the values of \( z \) extend to the left of 4.

Graph Representation

• Draw a number line.
• Place a closed dot on \( 4 \).
• Shade the portion of the line to the left of \( 4 \), indicating all values less than or equal to \( 4 \).

Optional Changes

• If you need to change the endpoint from closed to open as per your instructions, you would change the dot at \( z = 4 \) to an open dot and restrict the shaded region:
  • In this case, it will indicate the solution is \( z < 4 \) instead, meaning \( z \) cannot equal \( 4 \).

Make sure to clarify what the final representation should be based on whether you want the original or the modified version!