Find all values of that satisfy . Give your answer as an interval.

Yes; a negative is less than a positive; that's why the answer includes the word "or"; the answer is either in the first section (less than the negative) or in the second section (more than the positive); it can't be in both.

x(x + 7.5) > 38

x² + 7.5x - 38 > 0

First, find the solutions of  x² + 7.5x - 38 = 0

I used the quadratic formula and got  x =  3.465  and  x  =  -10.965

These two numbers divide the x-axis into three groups.

So, there are three groups  (x <  -10.965)        (-10.965 < x < 3.465)       (x > 3.465)

Try any number from the first group; I'll choose -20; and put it back into the original inequality:

       x(x + 7.5) > 38     ===>     -20(-20 + 7.5)  =  250 and that's > 38 go this section works.

Try any number from the second group; I'll choose 0; and put it back into the original inequality:

       x(x + 7.5) > 38     ===>     0(0 + 7.5)  =  0 and that's not > 38 go this section doesn't works.

Try any number from the third group; I'll choose 10; and put it back into the original inequality:

       x(x + 7.5) > 38     ===>     10(10 + 7.5)  =  175 and that's > 38 go this section works.

Since the first group and the third group both work, the answer is:  x < -10.965  or  x > 3.465.

isnt' the negative less than a positive? So how can x be less than the -10.965 and greater than 3.465?

I think the answer that geno gave is incorrect. Sorry