Solve the inequality and graph the solution.

Question

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5≤c–9
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 \(-5 \leq c - 9\), we first isolate \(c\).

1. Add 9 to both sides of the inequality: \[ -5 + 9 \leq c \] \[ 4 \leq c \] or equivalently, \[ c \geq 4. \]

Graphing the Solution

1. On a number line, we will plot the point \(4\).
2. Since the inequality is \(c \geq 4\), we will close the endpoint at \(4\) because it is included in the solution.
3. The solution includes all numbers greater than \(4\), so we will draw a ray extending to the right from the point \(4\).

Summary

• Closed endpoint at \(4\).
• Ray extending to the right from \(4\).

Here is a rough sketch of how it should look:

<---|-----|-----|-----|-----|-----|-----|-----|-----|-----|----->
    1     2     3     4     5     6     7     8     9    10
                ●---------------------------------------------------->

• The dot on \(4\) is closed, indicating that \(4\) is part of the solution, and the arrow indicates all values greater than \(4\).