please check and correct thanks

Question

Problem: solve and check the inequality if possible
|4F+8|< 12
positive: negative:
|4F+8| < 12 |4F + 8| < -12
4F + 8 -8 < 12 - 8 4F +8-8 < -12-8
4F < 4 4F< -20
F < 1 F< -5
solutions 1 and -5 or
-5 < F < 1
check positive ck negative
|4F + 8| < 12 |4F + 8| < -12
4(1) + 8 < 12
4 + 8 < 12 4(-5) + 8 < -12
12 < 12 -20 +8 < -12
-12 < -12

Answer 1

Easier way:

4F + 8 < 12 AND -4F - 8 < 12
4F < 4 AND -4F < 20
F < 1 AND F > -5

so, ....
-5 < F < 1

(your check should include a value for each of the 3 regions , that is
F < -1
F between -1 and 5
F > 5

Answer 2

thank you so much for your help reiny. ann