Answer:
v = -28 and v = 12.
Explanation:
To solve the equation |v + 8| - 8 = -28, you can follow these steps:
First, add 8 to both sides of the equation to isolate the absolute value expression:
|v + 8| - 8 + 8 = -28 + 8
|v + 8| = -20
Now, you have an absolute value equation. There are two possible cases to consider:
Case 1: v + 8 is positive.
Case 2: v + 8 is negative.
Case 1 (v + 8 is positive):
In this case, the absolute value |v + 8| will be equal to its argument, which is (v + 8). So, you have:
v + 8 = -20
Subtract 8 from both sides:
v = -20 - 8
v = -28
Case 2 (v + 8 is negative):
In this case, the absolute value |v + 8| will be equal to the negation of its argument, which is -(v + 8). So, you have:
-(v + 8) = -20
To get rid of the negative sign, multiply both sides by -1:
v + 8 = 20
Now, subtract 8 from both sides:
v = 20 - 8
v = 12
So, there are two solutions to the equation:
v = -28 and v = 12.