Let's solve the inequality step by step:
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Start with the inequality: \[ 10(d + 6) - 10 \leq 10 \]
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Distribute the 10 on the left side: \[ 10d + 60 - 10 \leq 10 \] Simplifying gives: \[ 10d + 50 \leq 10 \]
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Subtract 50 from both sides: \[ 10d \leq 10 - 50 \] Simplifying gives: \[ 10d \leq -40 \]
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Divide both sides by 10: \[ d \leq -4 \]
The solution to the inequality is: \[ d \leq -4 \]
Graphing the Solution
To graph this solution on a number line:
- Plot the point at \(-4\).
- Since the inequality is \(d \leq -4\), we will use a closed dot at \(-4\) (indicating that \(-4\) is included in the solution).
- Shade to the left of \(-4\) to indicate that all numbers less than \(-4\) are included in the solution.
Changing the Endpoint and Deleting a Segment
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Change from closed to open: Let's change the endpoint from closed to open. So, we will make the dot at \(-4\) open, indicating that \(-4\) is not included in the solution.
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To fulfill the instruction to delete the middle of the segment, let's say we delete the segment starting from the open dot at \(-4\) extending to the left since our solution is \((-\infty, -4)\) without including \(-4\).
Thus, the final graph will be:
- An open circle at \(-4\).
- Shaded to the left towards negative infinity, indicating that all values less than \(-4\) are part of the solution, but \(-4\) itself is not included.
This reflects the solution \(d < -4\) in a visual manner.
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