Which of the following is the value of x in the equation below.
(|2x – 4| – 10 = 2)
A.
x=4 or x=-8
B.
x=-4 or x=8
C.
x=-2 or x=1
D.
x=-3 or x=5
To solve the equation ∣2x−4∣−10=2|2x – 4| – 10 = 2∣2x−4∣−10=2, follow these steps:
- Isolate the Absolute Value:∣2x−4∣−10=2|2x – 4| – 10 = 2∣2x−4∣−10=2Add 10 to both sides:∣2x−4∣=12|2x – 4| = 12∣2x−4∣=12
- Solve the Absolute Value Equation: The equation ∣2x−4∣=12|2x – 4| = 12∣2x−4∣=12 means that:2x−4=12or2x−4=−122x – 4 = 12 \quad \text{or} \quad 2x – 4 = -122x−4=12or2x−4=−12For 2x−4=122x – 4 = 122x−4=12:2x−4=122x – 4 = 122x−4=12Add 4 to both sides:2x=162x = 162x=16Divide by 2:x=8x = 8x=8For 2x−4=−122x – 4 = -122x−4=−12:2x−4=−122x – 4 = -122x−4=−12Add 4 to both sides:2x=−82x = -82x=−8Divide by 2:x=−4x = -4x=−4
- Conclusion: The values of xxx are x=8x = 8x=8 and x=−4x = -4x=−4.
Thus, the correct answer is B. x = -4 or x = 8.