Solve the inequality and graph the solution.

Question

9(m–1)–10<8
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 \( 9(m - 1) - 10 < 8 \), we will first simplify the inequality.

1. Distribute \( 9 \) into \( (m - 1) \):

   \[ 9m - 9 - 10 < 8 \]

2. Combine like terms:

   \[ 9m - 19 < 8 \]

3. Add \( 19 \) to both sides:

   \[ 9m < 8 + 19 \] \[ 9m < 27 \]

4. Divide both sides by \( 9 \):

   \[ m < 3 \]

Now, we have \( m < 3 \) as the solution.

Graphing the Solution

1. Endpoints: The endpoint in this case is the number \( 3 \).
2. Open or Closed Endpoint: Since the inequality is \( m < 3 \) (not less than or equal), we will use an open endpoint at \( 3 \).
3. Middle Segment: Since there is no middle segment to delete, we simply graph the solution directionally from the endpoint.

Graph Representation

• To graph the solution \( m < 3 \):
  • Mark an open circle at \( 3 \) (to indicate that \( 3 \) is not included in the solution);
  • Shade to the left of \( 3 \) to represent all values less than \( 3 \).

The final graph will look like this:

<---o========================
     3

The open circle at \( 3 \) indicates that \( 3 \) is not included in the solution, and the shaded line to the left indicates all numbers less than \( 3 \) are part of the solution.