Question

1. |38| - 4 = 11

Explanation:

Step1: Analyze the equation

We have the equation \(|3x| - 4 = 11\). First, we need to isolate the absolute value term.

Step2: Add 4 to both sides

Add 4 to each side of the equation: \(|3x| - 4 + 4 = 11 + 4\), which simplifies to \(|3x| = 15\).

Step3: Solve the absolute value equation

The absolute value equation \(|3x| = 15\) means that \(3x = 15\) or \(3x = -15\).

Step4: Solve for x in each case

For \(3x = 15\), divide both sides by 3: \(x = \frac{15}{3} = 5\).
For \(3x = -15\), divide both sides by 3: \(x = \frac{-15}{3} = -5\).

Answer:

The solutions are \(x = 5\) or \(x = -5\)