Can someone help me with this calculus question?

The solution will be the intersection of two separate problems:

5 < | 7x + 9 |  and | 7x + 9 | < 10

for the first:
this becomes:
5 < 7x + 9 ==> -4 < 7x ==> x > -4/7
or
-5 > 7x + 9 ==> -14 > 7x ==> x < -2

for the second:
| 7x + 9 | < 10 becomes: -10 < 7x + 9 < 10
-19 < 7x < 1
-19/7 < x < 1/7

now we have three intervals, and we need the intersection of the second with the union of the first:
[(-inf , -2) U (-4/7 , inf)] and (-19/7 , 1/7)

the solution is:
(-19/7 , -2) U (-4/7 , 1/7) <===== solution

you can confirm this graphically...
Plot | 7x + 9 |, 5, and 10 as Y1, Y2, and Y3
Look for the parts of the absolute value graph that fall between 5 and 10
the intervals are those found algebraically above

You have two cases:
5 < 7x + 9 < 10 _______and______ -5 > 7x + 9 > -10 (the - reverses the inequality)
-4 < 7x < 1 _____and_____ -14 > 7x > -19
-4/7 < x < 1/7 _____ and _____ -2 > x > -19/7
(-4/7, 1/7) _____ and _____ (-19/7, -2)