Question

solve.\\(|3x + 1| - 6 = -3\\(x = square\\)(simplify your answer. type an integer or a fraction. use a comma to separate answers.)

Explanation:

Step1: Isolate the absolute value

Add 6 to both sides of the equation \(|3x + 1| - 6 = -3\) to get \(|3x + 1| = -3 + 6\).
\(|3x + 1| = 3\)

Step2: Solve the absolute value equation

The absolute value equation \(|A| = B\) (where \(B\geq0\)) is equivalent to \(A = B\) or \(A = -B\). So we have two cases:

Case 1: \(3x + 1 = 3\)

Subtract 1 from both sides: \(3x = 3 - 1\)
\(3x = 2\)
Divide both sides by 3: \(x = \frac{2}{3}\)

Case 2: \(3x + 1 = -3\)

Subtract 1 from both sides: \(3x = -3 - 1\)
\(3x = -4\)
Divide both sides by 3: \(x = -\frac{4}{3}\)

Answer:

\(\frac{2}{3}, -\frac{4}{3}\)