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Consider the following absolute value inequality:

[tex]\[ |9x + 1| \ \textless \ 12 \][/tex]

Step 1: Rewrite the given inequality as two linear inequalities.

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GinnyAnswer
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.
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