Final answer:
The solution to the inequality 9(p - 9) + 7 > -2 is p > 8. On a graph, this is represented by an open circle at p = 8 and shading to the right indicating all p-values greater than 8.
Step-by-step explanation:
To solve the inequality 9(p - 9) + 7 > -2, first distribute the 9 into the parentheses:
9p - 81 + 7 > -2
Next, combine like terms on the left side of the inequality:
9p - 74 > -2
Now, add 74 to both sides of the inequality to isolate the term with p on one side:
9p > 72
Divide both sides by 9 to find the p-value:
p > 8
To sketch a graph of this situation, draw a number line with an open circle at 8 to indicate that 8 is not included in the solution set. Then, shade the area to the right of 8 to represent all numbers greater than 8.
Label and scale the x-axis accordingly, and mark the point p = 8 clearly on the axis.