Let's solve the inequality step by step.
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Distribute and simplify the expression: \[ 12(c - 1) + 44 \leq 80 \] Distributing the 12: \[ 12c - 12 + 44 \leq 80 \] Combining like terms: \[ 12c + 32 \leq 80 \]
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Isolate the variable \(c\): Subtract 32 from both sides: \[ 12c \leq 80 - 32 \] \[ 12c \leq 48 \] Now, divide both sides by 12: \[ c \leq 4 \]
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Graph the inequality: The solution \(c \leq 4\) means that \(c\) includes all values less than or equal to 4.
- Endpoints: The endpoint is \(c = 4\).
- Since the inequality is less than or equal to \(4\), we will use a closed dot at \(4\) to indicate that \(4\) is included in the solution.
To graph this:
- Draw a number line.
- Mark the point \(4\) with a closed dot.
- Shade everything to the left of \(4\) to indicate that all values less than \(4\) are included.
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Selecting an endpoint to change from closed to open: Since the inequality includes the endpoint, it will remain a closed endpoint, so there is no selection to change it from closed to open here.
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Select the middle of the segment to delete: Since this is a one-sided inequality (c ≤ 4), we note that there is no middle segment to delete.
Final Representation:
- The graph shows a closed dot at \(4\) and shading to the left, indicating all values less than or equal to \(4\) are part of the solution.
So the solution is: \[ c \leq 4 \]
Graph:
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4
(The dot at 4 is closed, and the line continues to the left.)