Solve the inequality and graph the solution.

Question

2(v+7)+1<11
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 \( 2(v + 7) + 1 < 11 \), we can follow these steps:

1. Distribute: \[ 2(v + 7) = 2v + 14 \] The inequality now becomes: \[ 2v + 14 + 1 < 11 \]

2. Combine like terms: \[ 2v + 15 < 11 \]

3. Isolate the variable: Subtract 15 from both sides: \[ 2v < 11 - 15 \] \[ 2v < -4 \]

4. Divide by 2: \[ v < -2 \]

The solution to the inequality is \( v < -2 \).

Graphing the Solution

1. Endpoints: The endpoint for this inequality is \( -2 \).

2. Open or Closed: Since the inequality is strictly less than (<), we will use an open circle at \( -2 \) to indicate that this endpoint is not included in the solution.

3. Ray: The solution is a ray extending to the left from \( -2 \), representing all values less than \( -2 \).

Summary of the Graph

• Draw an open circle at \( -2 \).
• Shade the line to the left of \( -2 \) to indicate that all values less than \( -2 \) are included in the solution.

Here's a basic representation of the graph:

<----( -2 )---->

In this representation:

• The parentheses at \( -2 \) indicate that it is an open endpoint, meaning \( -2 \) is not part of the solution set. The arrow indicates that the shading extends infinitely left, representing all values less than \( -2 \).