Question

14.
Solve the inequality.
|3x+6|<12

Answer 1

To solve the inequality \( |3x + 6| < 12 \), we start by breaking it into two separate inequalities without the absolute value:

1. \( 3x + 6 < 12 \)
2. \( 3x + 6 > -12 \)

### 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:
\[
(-6, 2)
\]