Question

Solve \(|3 x+3|>12.\) (A) \(-5 < x < 3\) (B) \(3 < x < -5\) (C) \(x >3\) or \(x < -5\) (D) \(x >3\)

Short answer

The correct answer is (C) \(x >3\) or \(x < -5\).

Step-by-step solution

Isolate the Absolute Value

Given the inequality \(|3x + 3| > 12\), the first task is to isolate the absolute value. In this case, it is already isolated which makes this step easier.

Separate into Two Inequalities

The definition of absolute value leads to the formation of two inequalities: \(3x + 3 > 12\) and \(3x + 3 < -12\).

Solve First Inequality

To solve the first inequality, you subtract 3 from both sides to get \(3x > 9\), then divide each side by 3 to obtain \(x > 3\).

Solve Second Inequality

To solve the second inequality, you again subtract 3 from both sides to get \(3x < -15\), then divide both sides by 3 to obtain \(x < -5\).

Combine Solutions

The solution to the given inequality is the union of the solutions to both inequalities from steps 3 and 4. Hence, the solution is \(x > 3\) or \(x < -5\).