Solve the inequality and graph the solution.

Question

12≥6d
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 \(12 \geq 6d\):

1. Divide both sides by 6 (since 6 is positive, the direction of the inequality does not change): \[ \frac{12}{6} \geq d \implies 2 \geq d \implies d \leq 2 \]

So, the solution to the inequality is \(d \leq 2\).

2. Endpoint: The endpoint is 2. Since the inequality includes \(=\), we will use a closed circle at 2.

3. Graphing:

   • Draw a number line.
   • Mark the endpoint at \(2\) with a closed circle (indicating that 2 is included in the solution).
   • Shade to the left of 2 (indicating all numbers less than or equal to 2 are included in the solution).

4. Changing from closed to open: According to your request, let’s change the endpoint from closed to open. We will mark it with an open circle instead (indicating 2 is not included).

5. Select the middle of the segment: We will erase the segment that represents all values less than 2, which implies we are left with all the values greater than 2.

Thus, the final graph step:

• Mark open circle at 2.
• Shade to the right of 2 (indicating all numbers greater than 2 since we are deleting the part that goes to the left of 2).

So the resultant solution after applying your transformations is the inequality \(d > 2\), and the graph will represent that.