solve the absolute value equation. select the two solutions of the equation.
-3|2x-1|=-15
A No Solution
B 2
C -3
D -2
E -5
F 3
To solve the absolute value equation -3|2x-1|=-15, we can begin by isolating the absolute value expression by dividing both sides of the equation by -3:
|2x-1| = (-15)/(-3)
|2x-1| = 5
Now, we can split the equation into two separate cases:
Case 1: 2x-1 is positive
When 2x-1 is positive, |2x-1| simplifies to 2x-1. Therefore,
2x-1 = 5
2x = 5+1
2x = 6
x = 6/2
x = 3
Case 2: 2x-1 is negative
When 2x-1 is negative, |2x-1| simplifies to -(2x-1), which can be written as -2x+1. Therefore,
-2x+1 = 5
-2x = 5-1
-2x = 4
x = 4/(-2)
x = -2
Thus, the two solutions of the equation are x = 3 (option F) and x = -2 (option D).