To solve the inequality \( |3x + 6| < 12 \), we start by breaking it into two separate inequalities without the absolute value:
- \( 3x + 6 < 12 \)
- \( 3x + 6 > -12 \)
Solving the first inequality:
\[ 3x + 6 < 12 \] Subtract 6 from both sides: \[ 3x < 6 \] Now, divide by 3: \[ x < 2 \]
Solving the second inequality:
\[ 3x + 6 > -12 \] Subtract 6 from both sides: \[ 3x > -18 \] Now, divide by 3: \[ x > -6 \]
Combining the results:
The solution to the inequality \( |3x + 6| < 12 \) is the combination of both inequalities: \[ -6 < x < 2 \]
Final answer:
The solution is: \[ (-6, 2) \]