Questions: Consider the following inequality: x-4<0 Solve the absolute value inequality and express the solution in interval notation.

Solution Steps

To solve the absolute value inequality \(|x| - 4 < 0\), we need to isolate the absolute value expression and then consider the definition of absolute value. The inequality \(|x| < 4\) means that \(x\) must be within 4 units of 0 on the number line. This translates to the interval \(-4 < x < 4\).

Given the inequality: \[ |x| - 4 < 0 \] we first isolate the absolute value expression: \[ |x| < 4 \]

The inequality \(|x| < 4\) means that \(x\) must be within 4 units of 0 on the number line. This translates to: \[ -4 < x < 4 \]

Final Answer