180k views
0 votes
Can someone please help me solve
|b|\ \textless \ 3

1 Answer

4 votes

9514 1404 393

Answer:

-3 < b < 3

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

_____

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.

User AndreaNobili
by
4.5k points