The picture you've included only shows the first two problems, but I'll still answer them for you anyways. If you update it to show the rest, then just tell me and I'll finish the rest of it. :)
1) First subtract 4 to represent the 4 extra ones she made to get 45.
Then divide by 1 1/2 to represent 1 1/2 for each student to get 30.
So there must be less than or equal to 30 students in the class, and the sign that represents that is ≤. The answer is D, and Sam is Correct!
2) A. True, correct inequality sign.
B. False, the one for A is the right one.
C. True, 7 + 3.5(which is half of 7) is 10.5- less than 15.
D. False, 3 times 7 is 21- more than 15.
Hope this helps!