9514 1404 393
Answer:
-3 < b < 3
Step-by-step explanation:
The inequality is equivalent to two inequalities.
For b ≥ 0, this is ...
b < 3
Together with the restriction that b ≥ 0, the solution to this is ...
0 ≤ b < 3
__
For b ≤ 0, this is ...
-b < 3
b > -3 . . . . multiply by -1
Together with the restriction that b ≤ 0, the solution to this is ...
-3 < b ≤ 0
__
The solution is the 'or' of these two solutions. They can be expressed as the single compound inequality ...
-3 < b < 3
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Comment on absolute value inequalities
When the inequality is of the form ...
|p| < q
It can be written as the equivalent compound inequality ...
-q < p < q
as we showed above.
