Solve the following absolute value inequality:

Question

|2x+3|>4

(1 point)
Responses

x<−1 or x>7
x<−1 or x>7

x<4/3 or x>−3/2
x<4/3 or x>−3/2

x<−7/2 or x>1/2
x<−7/2 or x>1/2

x<−7 or x>1

Answer 1

To solve the absolute value inequality \( |2x + 3| > 4 \), we can break it down into two cases:

1. \( 2x + 3 > 4 \)
2. \( 2x + 3 < -4 \)

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

Subtract 3 from both sides: \[ 2x > 1 \] Now divide by 2: \[ x > \frac{1}{2} \]

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

Subtract 3 from both sides: \[ 2x < -7 \] Now divide by 2: \[ x < -\frac{7}{2} \]

Combining both cases, we have the solution: \[ x < -\frac{7}{2} \quad \text{or} \quad x > \frac{1}{2} \]

Therefore, the correct response from the provided options is: x < -7/2 or x > 1/2