Which represents the solution to the absolute value equation?
2|x+2|−1=5
(1 point)
Responses
x = 1 or x = -1
x = 1 or x = -1
x = 1 or x = -5
x = 1 or x = -5
x = 4 or x = -8
x = 4 or x = -8
x = 5 or x = -5
The solution to the absolute value equation 2|x+2|−1=5 is x = 1 or x = -5.
To find the solution to the absolute value equation 2|x+2|−1=5, follow these steps:
Step 1: Add 1 to both sides of the equation:
2|x+2| = 6
Step 2: Divide both sides of the equation by 2:
|x+2| = 3
Step 3: Set up two separate equations, one positive and one negative, representing the absolute value:
x+2 = 3 or x+2 = -3
Step 4: Solve each equation separately:
For x+2 = 3, subtract 2 from both sides:
x = 1
For x+2 = -3, subtract 2 from both sides:
x = -5
Therefore, the solution to the absolute value equation 2|x+2|−1=5 is x = 1 or x = -5.