Solve the inequality and graph the solution.

Question

18≥2(q+17)
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 \( 18 \geq 2(q + 17) \), we start by simplifying it step by step.

1. Distribute the 2 on the right side: \[ 18 \geq 2q + 34 \]

2. Subtract 34 from both sides: \[ 18 - 34 \geq 2q \] \[ -16 \geq 2q \]

3. Divide by 2 (remember that dividing by a positive number does not change the inequality sign): \[ -8 \geq q \]

This can be rewritten as: \[ q \leq -8 \]

Graphing the Solution

The solution \( q \leq -8 \) means that \( q \) can take any value less than or equal to \(-8\).

• Endpoint: The endpoint is \(-8\).
• Since we have \( q \leq -8\), this endpoint will be closed (indicating that \(-8\) is included in the solution).
• Direction: The solution will be towards the left, meaning all values less than -8.

Final Representation

On a number line:

• A closed dot (●) is placed at \(-8\) to indicate that \(-8\) is included.
• A line extends to the left from \(-8\) to indicate all values less than \(-8\).

Annotation

• Endpoint: -8 (closed dot)
• Ray direction: Leftward, indicating all values less than -8.

Here is how you would describe it on the graph:

• Place a closed dot at \(-8\).
• Draw an arrow pointing left from \(-8\) to indicate that values are included all the way to negative infinity.

Example of Graph Representation

<-----●=========>
      -8

This visual means the solution set includes \(-8\) and all numbers to the left of it.