To solve the equation −4 |3v| = 24 for v, we need to isolate v.
Let's break it down step by step:
1. Remove the absolute value by considering two cases:
a. Case 1: 3v ≥ 0
In this case, the absolute value can be removed, and the equation becomes:
-4(3v) = 24
b. Case 2: 3v < 0
In this case, the absolute value becomes its negation, and the equation becomes:
-4(-3v) = 24
2. Simplify each case:
a. Case 1: -4(3v) = 24
-12v = 24
Divide both sides by -12: v = 24 / -12
v = -2
b. Case 2: -4(-3v) = 24
12v = 24
Divide both sides by 12: v = 24 / 12
v = 2
Therefore, the solutions to the equation are v = -2 and v = 2.