|2х+3|>4

To solve the inequality \( |2x + 3| > 4 \), we can consider two separate cases based on the definition of absolute value.

Case 1: \( 2x + 3 > 4 \)

1. Subtract 3 from both sides: \[ 2x > 1 \]

2. Divide both sides by 2: \[ x > \frac{1}{2} \]

Case 2: \( 2x + 3 < -4 \)

1. Subtract 3 from both sides: \[ 2x < -7 \]

2. Divide both sides by 2: \[ x < -\frac{7}{2} \]

Solution

Combining both cases, the solution to the inequality \( |2x + 3| > 4 \) is: \[ x < -\frac{7}{2} \quad \text{or} \quad x > \frac{1}{2} \]

In interval notation, the solution can be expressed as: \[ (-\infty, -\frac{7}{2}) \cup \left(\frac{1}{2}, \infty\right) \]

This represents the values of \( x \) that satisfy the original inequality.