Solve for v.

|–2v| = 8


Write your answers as integers or as proper or improper fractions in simplest form.

v = 
 or v = 


To solve the equation \( |–2v| = 8 \), we need to consider the property of absolute values, which says that \( |x| = a \) means \( x = a \) or \( x = -a \).

### Step-by-Step Solution:

1. Start with the given equation:
   \[
   |–2v| = 8
   \]
   
2. This means:
   \[
   –2v = 8 \quad \text{or} \quad –2v = -8
   \]

3. Solve both cases separately:

   **Case 1:**
   \[
   –2v = 8
   \]
   Divide both sides by –2:
   \[
   v = \frac{8}{–2} = –4
   \]

   **Case 2:**
   \[
   –2v = –8
   \]
   Divide both sides by –2:
   \[
   v = \frac{–8}{–2} = 4
   \]

### Final Answer:
\[
v = –4 \quad \text{or} \quad v = 4
\]

Would you like more details on any part of this solution? Here are some related questions:

1. How do we solve absolute value equations with more complex expressions?
2. What are the basic properties of absolute values?
3. Can absolute values ever be negative?
4. How do you check your solutions for absolute value equations?
5. What are some real-world applications of absolute value equations?

**Tip:** Always remember that absolute value equations can have two potential solutions, one positive and one negative.

|–2v| = 8. Solve for v. Write your answers as integers or as proper or improper fractions in simplest form.

Learn how to solve the absolute value equation |–2v| = 8 with step-by-step guidance. This problem focuses on the properties of absolute value equations and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation