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 possible cases for the absolute value expression.

1. **Case 1:** \( 2x + 1 = 5 \)
- Subtract 1 from both sides:
\[
2x = 5 - 1 \\
2x = 4
\]
- Divide by 2:
\[
x = \frac{4}{2} = 2
\]

2. **Case 2:** \( 2x + 1 = -5 \)
- Subtract 1 from both sides:
\[
2x = -5 - 1 \\
2x = -6
\]
- Divide by 2:
\[
x = \frac{-6}{2} = -3
\]

Thus, the solutions to the equation \( |2x + 1| = 5 \) are \( x = 2 \) and \( x = -3 \).

So the final answer is:
**x = 2, -3**.