https://file.aiquickdraw.com/mathbot/file/1729017548392q04oeptz.jpg

The equation provided is:

\[
|v| + 15 = 24
\]

To solve for \( v \), follow these steps:

### Step 1: Isolate the Absolute Value
Subtract 15 from both sides of the equation:
\[
|v| = 24 - 15
\]
\[
|v| = 9
\]

### Step 2: Solve the Absolute Value Equation
The equation \( |v| = 9 \) implies that \( v \) can be either \( 9 \) or \( -9 \), since the absolute value of both is 9.

Therefore, the solutions are:
\[
v = 9 \quad \text{or} \quad v = -9
\]

### Final Answer:
\[
v = 9 \quad \text{and} \quad v = -9
\]

Would you like more details on any of these steps, or do you have further questions?

Here are some related questions that might interest you:
1. How do you solve equations involving absolute values with variables on both sides?
2. What are some methods to check if the solutions to absolute value equations are correct?
3. How do you graph the equation \( |v| + 15 = 24 \)?
4. What happens if the right side of the absolute value equation is negative?
5. How do you handle equations with multiple absolute value terms?

**Tip:** When solving absolute value equations, always consider both the positive and negative solutions for the expression within the absolute value.

Learn how to solve the absolute value equation |v| + 15 = 24 with a step-by-step solution. This algebra problem covers key concepts such as isolating the absolute value and finding both positive and negative solutions. Suitable for students in Grades 6-8.

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