To solve the inequality \( 20(k - 2) - 20 \geq 20 \), we can start by simplifying it step-by-step.
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Distribute the \( 20 \): \[ 20k - 40 - 20 \geq 20 \]
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Combine like terms: \[ 20k - 60 \geq 20 \]
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Add \( 60 \) to both sides: \[ 20k \geq 80 \]
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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:
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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.
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Open or Closed: Since the inequality is non-strict (≥), we keep the endpoint \( 4 \) closed.
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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.