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Solve the inequality.

| 3x + 6 | < 12



–21 < x < 3

–2 < x < 2

–6 > x > 2

–6 < x < 2

1 answer

To solve the inequality \( |3x + 6| < 12 \), we can start by rewriting the absolute value inequality into two separate cases:

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

Now, let's solve each inequality:

Case 1: \[ 3x + 6 < 12 \] Subtracting 6 from both sides: \[ 3x < 6 \] Dividing by 3: \[ x < 2 \]

Case 2: \[ 3x + 6 > -12 \] Subtracting 6 from both sides: \[ 3x > -18 \] Dividing by 3: \[ x > -6 \]

Now, we can combine the results from both cases: \[ -6 < x < 2 \]

Thus, the solution to the inequality \( |3x + 6| < 12 \) is: \[ -6 < x < 2 \]

Therefore, the correct answer is: \[ -6 < x < 2 \]