|х+2|>3

To solve the inequality \(|x + 2| > 3\), we need to consider the two cases in which the absolute value expression can be satisfied:

Case 1: \(x + 2 > 3\)

1. Solve for \(x\): \[ x + 2 > 3 \] Subtract 2 from both sides: \[ x > 1 \]

Case 2: \(x + 2 < -3\)

1. Solve for \(x\): \[ x + 2 < -3 \] Subtract 2 from both sides: \[ x < -5 \]

Final Solution

Combining the two cases, the solution to the inequality \(|x + 2| > 3\) is: \[ x < -5 \quad \text{or} \quad x > 1 \]

In interval notation, this can be expressed as: \[ (-\infty, -5) \cup (1, \infty) \]