Question

Solve the inequality.

|3x + 6| < 12


–6 > x > 2


–6 < x < 2


–2 < x < 2


–21 < x < 3

Answer 1

To solve the inequality \(|3x + 6| < 12\), we start by considering the definition of absolute value. The inequality \(|A| < B\) implies that \(-B < A < B\).

So, we can rewrite the inequality as:

\[
-12 < 3x + 6 < 12
\]

Now we will split this into two separate inequalities:

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

### Solving the first inequality:

\[-12 < 3x + 6\]

Subtracting 6 from both sides:

\[-12 - 6 < 3x\]

\[-18 < 3x\]

Dividing by 3:

\[-6 < x\]

### Solving the second inequality:

\[3x + 6 < 12\]

Subtracting 6 from both sides:

\[3x < 12 - 6\]

\[3x < 6\]

Dividing by 3:

\[x < 2\]

### Combining the results:

We now combine the inequalities:

\[-6 < x < 2\]

Thus, the solution to the inequality \(|3x + 6| < 12\) is

\(-6 < x < 2\).

The correct answer from your options is:

**–6 < x < 2**