Solve the inequality and graph the solution.

Question

14>7(d–6)
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

Let's solve the inequality step by step:

1. Start with the inequality: \[ 14 > 7(d - 6) \]

2. Distribute the 7 on the right side: \[ 14 > 7d - 42 \]

3. Add 42 to both sides to isolate the term with \( d \): \[ 14 + 42 > 7d \] \[ 56 > 7d \]

4. Now, divide both sides by 7: \[ \frac{56}{7} > d \] \[ 8 > d \quad \text{or} \quad d < 8 \]

So, the solution to the inequality is \( d < 8 \).

Graphing the Solution

• The solution \( d < 8 \) means that \( d \) can take any value less than 8.
• You plot this on a number line:

1. Draw a number line.
2. Mark the point 8.
3. Since the inequality is \( d < 8 \), you will use an open circle at 8 to indicate that 8 is not included in the solution.
4. Shade the line to the left of 8 (as this indicates all values less than 8).

Summary of the Graphing Steps:

• Closed at \( 8 \) since it is not included (open circle).
• Shade to the left of 8.

The final solution set can be represented as \( (-\infty, 8) \).