Solve the inequality and graph the solution.

Question

c+7
6
≤1
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 \( \frac{c + 7}{6} \leq 1 \), follow these steps:

1. Multiply both sides by 6 to eliminate the fraction (since 6 is positive, the direction of the inequality remains the same):

   \[ c + 7 \leq 6 \]

2. Subtract 7 from both sides:

   \[ c \leq 6 - 7 \] \[ c \leq -1 \]

Now we have the solution:

\[ c \leq -1 \]

This means that the values of \(c\) can include all numbers less than or equal to -1.

Graphing the Solution

1. Identify the endpoint: The endpoint here is \(-1\).
2. Plot the endpoint: Since the inequality is \(\leq\), we will use a closed circle at -1 (indicating that -1 is included in the solution).
3. Shade the region: Shade to the left of -1 to indicate all the values less than -1.

Adjustments

If we want to change the endpoint to open (not included in the solution), we would change the inequality to \(c < -1\), which results in an open circle at -1. However, since the problem requires us to keep \(c \leq -1\), we maintain the closed circle.

Final Graph:

• Closed Circle at \(-1\)
• Shaded region to the left extending infinitely.

This is how you would represent the solution graphically. If you choose to change the inequality and make it \(c < -1\), you would use an open circle. For the purpose of this solution, since we kept \(c \leq -1\), you will essentially present it as:

• Closed circle at \(-1\).
• Shaded to the left towards negative infinity.