Question

Solve for all values of x in simplest form:

1−2∣x−8∣=−19
A) x = 27
B) x = 11
C) x = 3.5
D) x = -9

Answer 1

To solve the equation 1−2∣x−8∣=−19, isolate the absolute value expression and consider two cases: x-8 is positive and x-8 is negative. The solutions are x=18 and x=-2.

Step-by-step explanation:

To solve the equation 1−2∣x−8∣=−19, we can start by isolating the absolute value expression. We can rewrite the equation as 1=−19+2∣x−8∣. Then, we can subtract -19 from both sides to get 20=2∣x−8∣. Next, we divide both sides by 2 to get 10=∣x−8∣. Now, we have two cases to consider:

1. Case 1: x-8 is positive. In this case, we have x-8=10. Adding 8 to both sides, we get x=18.

2. Case 2: x-8 is negative. In this case, we have -(x-8)=10. Simplifying, we get -x+8=10. Subtracting 8 from both sides, we get -x=2. Multiplying both sides by -1, we get x=-2.

Therefore, the solutions to the equation are x=18 and x=-2.