Question

Solve the following absolute value inequality:

|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**