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Solve the inequality and graph the solution.

–
(n–3)>1
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.

1 answer

To solve the inequality \( n - 3 > 1 \), we can follow these steps:

  1. Isolate \( n \): \[ n - 3 > 1 \] Add 3 to both sides: \[ n > 1 + 3 \] Simplifying the right side gives: \[ n > 4 \]

  2. Graph the solution: The solution \( n > 4 \) means that \( n \) can take on any value greater than 4. To represent this graphically:

    • We plot an open circle (indicating that 4 is not included) at the point \( n = 4 \).
    • We then draw a ray or line extending to the right from the open circle to indicate all numbers greater than 4.

Here's the description of the plot:

  • Open Circle at 4: This indicates that 4 is not included in the solution.
  • Ray extending right: Indicating all values greater than 4.

If you visualize this on a number line, it looks like this:

  <-----|-----|-----|-----|-----|-----|-----|----->
       1     2     3     4     5     6     7
                 (=========>

Where:

  • The parentheses \( ( \) around 4 indicate it's an open endpoint (not including 4).
  • The arrow indicates all values greater than 4 are included in the solution.