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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

1 answer

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.