please check and correct thanks
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
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
thank you so much for your help reiny. ann
The solution to the inequality |4F+8| < 12 is -5 < F < 1. To solve this inequality, we follow these steps:
1. Split the inequality into two cases: one for positive values inside the absolute value and one for negative values inside the absolute value.
Positive Case:
|4F + 8| < 12
4F + 8 - 8 < 12 - 8
4F < 4
F < 1
Negative Case:
|4F + 8| < -12
This case is not possible since the absolute value cannot be negative.
Therefore, the solution is F < 1 for the positive case.
To check the solution, we substitute values from within the range -5 to 1 back into the original inequality:
Case F = 1 (Positive Case):
|4(1) + 8| < 12
12 < 12
This is not true, so the value F = 1 is not a solution.
Case F = -5 (Negative Case):
|4(-5) + 8| < 12
|-20 + 8| < 12
|-12| < 12
12 < 12
This is not true, so the value F = -5 is also not a solution.
Therefore, the correct solution to the inequality is -5 < F < 1.