To start solving the absolute value inequality [tex]\(|9x + 1| < 12\)[/tex], we need to understand that an absolute value inequality of the form [tex]\(|A| < B\)[/tex] can be rewritten as two separate linear inequalities:
[tex]\[
-B < A < B
\][/tex]
For our specific inequality, we have [tex]\(A = 9x + 1\)[/tex] and [tex]\(B = 12\)[/tex]. Therefore, we can rewrite [tex]\(|9x + 1| < 12\)[/tex] as:
[tex]\[
-12 < 9x + 1 < 12
\][/tex]
This can be split into two separate linear inequalities:
1. [tex]\(-12 < 9x + 1\)[/tex]
2. [tex]\(9x + 1 < 12\)[/tex]
These are our two linear inequalities that represent the original absolute value inequality.
