Solve the inequality and graph the solution.

Question

20(k–2)–20≥20
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 \( 20(k - 2) - 20 \geq 20 \), we can start by simplifying it step-by-step.

1. Distribute the \( 20 \): \[ 20k - 40 - 20 \geq 20 \]

2. Combine like terms: \[ 20k - 60 \geq 20 \]

3. Add \( 60 \) to both sides: \[ 20k \geq 80 \]

4. Divide by \( 20 \): \[ k \geq 4 \]

So, the solution to the inequality is \( k \geq 4 \).

Graphing the Solution

To graph this solution on a number line:

1. Endpoints: The endpoint of the solution \( k = 4 \) is included in the solution because it has a "greater than or equal to" sign (≥). Therefore, at \( k = 4 \), we will use a closed circle.

2. Open or Closed: Since the inequality is non-strict (≥), we keep the endpoint \( 4 \) closed.

3. Middle of the Segment: The solution indicates all values to the right of \( k = 4 \). So, we will graph it with an arrow extending to the right, indicating all values greater than \( 4 \).

Final Graph

• A closed circle at \( 4 \)
• An arrow extending to the right of \( 4 \)

Here’s how you can visualize it:

  <---|----|----|----|----|----|----|----|----|----->
      1    2    3    4    5    6    7    8
           ●------------------------->

• The dot at \( 4 \) represents that \( 4 \) is included in the solution.
• The arrow indicates that all values greater than \( 4 \) are also solutions to the inequality.