Answer:
[tex]-3<v<9[/tex]
Step-by-step explanation:
The inequality [tex]|3-v| < 6[/tex] is equivalent to the system of two inequalities:
[tex]\left\{\begin{array}{l}3-v>-6\\ \\3-v<6\end{array}\right.[/tex]
Solve each inequality:
1. [tex]3-v>-6:[/tex]
[tex]3-v>-6\\ \\-v>-6-3\\ \\-v>-9\\ \\v<9[/tex]
2. [tex]3-v<6:[/tex]
[tex]-v<6-3\\ \\-v<3\\ \\v>-3[/tex]
The solution set to the initial inequality is
[tex]-3<v<9[/tex]
The graph of this solution set is attached.
