Final answer:
To solve the equation |v+8|-5=2, we move the 5 to the other side to isolate the absolute value, resulting in |v+8|=7.
Step-by-step explanation:
To solve the equation |v+8|-5=2, first, we need to isolate the absolute value expression by moving the 5 to the other side. This gives us |v+8|=2+5, which simplifies to |v+8|=7.
Next, we consider two possibilities since the absolute value of a number can be either positive or negative:
For the first case, subtract 8 from both sides to get v = -1. For the second case, subtract 8 from both sides to get v = -15. Therefore, the solutions to the equation are v = -1 and v = -15.
It's important to check these solutions in the original equation to ensure they make sense. After substituting the values of v back into the original equation, we see that both satisfy the equation, confirming that they are correct.