Final answer:
The student's inequality 105 > 7(a - 8) was solved by distributing and isolating the variable to find a < 23. The correct answer was not listed in the options. The graph would show an open circle at 23 with shading to the left, indicating all values less than 23 are included in the solution set.
Step-by-step explanation:
The student has asked to solve the inequality 105 > 7(a − 8) and graph the solution. To solve the inequality, we need to first distribute the 7 to both terms in the parenthesis, which simplifies the inequality to 105 > 7a − 56. Next, add 56 to both sides of the inequality to isolate the 7a on one side, resulting in 161 > 7a. Finally, divide both sides by 7 to solve for a, which gives us a < 23. This means option B, a > 15, is incorrect because we have found that a must be less than 23. The correct answer is not provided in the options given, but the approach to solve the inequality is demonstrated clearly.
To graph the solution, we draw a number line and represent all numbers less than 23. We place an open circle (not filled in) at 23 to indicate that 23 is not included in the solution set and shade to the left of the open circle to represent all the numbers that are less than 23.