We can solve this using the next property:
If a
Replace f (x) = - 2x- 5 , then:
-21 < f (x) < 0
-21 < -2x-5 < 0
Solve -21 < -2x-5 and -2x-5 < 0
Therefore:
-21 < -2x-5
Add both sides 5
-21+5 < -2x-5 +5
-16 < -2x
(-1)-16 < (-1)(-2x)
16>2x
x<16/2
x<8
and
-2x-5 < 0
Add both sides 5
-2x-5 +5 < 0+5
-2x<5
(-1)-2x < (-1)5
2x > -5
x > -5/2
Hence, the resulting interval is:
-5/2 < x < 8
