Question

Solve the following absolute value equation:

|2x+1|=5


(1 point)
Responses

x=2, −3
x=2, −3

x=5
x is equal to 5

x=6, −6
x=6, −6

x=3, −12

Answer 1

To solve the absolute value equation \(|2x + 1| = 5\), we need to consider the two cases that arise from the definition of absolute value.

### Case 1:
\[
2x + 1 = 5
\]
Subtracting 1 from both sides:
\[
2x = 4
\]
Dividing by 2:
\[
x = 2
\]

### Case 2:
\[
2x + 1 = -5
\]
Subtracting 1 from both sides:
\[
2x = -6
\]
Dividing by 2:
\[
x = -3
\]

Thus, the solutions to the equation \(|2x + 1| = 5\) are:
\[
x = 2 \quad \text{and} \quad x = -3
\]

The correct response is:
**x=2, −3**