the minimum distance between two fence posts is 4 feet. the maximum distance is 10. write an absolute value equation that represents the minimum and maximum distance

To represent the minimum and maximum distance between two fence posts using an absolute value equation, we can define the midpoint between the minimum and maximum distances as the center, and the deviation from this midpoint as the absolute value.

The minimum distance is 4 feet, and the maximum distance is 10 feet.

1. **Midpoint Calculation**:  
   The midpoint \( c \) between 4 and 10 is calculated as:
   \[
   c = \frac{4 + 10}{2} = \frac{14}{2} = 7 \text{ feet}
   \]

2. **Deviation Calculation**:  
   The deviation \( d \) from the midpoint is the difference between the midpoint and either the minimum or maximum value:
   \[
   d = 10 - 7 = 3 \text{ feet}
   \]

3. **Absolute Value Equation**:  
   The absolute value equation representing the distance \( x \) between the fence posts is:
   \[
   |x - 7| = 3
   \]

This equation means that the distance \( x \) is 3 feet away from the midpoint of 7 feet, which gives the range [4, 10].

Would you like more details or have any questions? Here are five related questions that might interest you:

1. How would you solve the absolute value equation \( |x - 7| = 3 \)?
2. What does the solution to \( |x - 7| = 3 \) represent graphically?
3. Can you write an inequality instead of an equation to represent this distance range?
4. How would the equation change if the minimum and maximum distances were different?
5. What if the distance range was represented by a different midpoint, how would that affect the equation?

**Tip:** Understanding the concept of the midpoint and deviation is crucial in setting up absolute value equations correctly, as they center the values and measure how far they can deviate from the midpoint.

Understand how to use an absolute value equation to calculate the minimum and maximum distances between fence posts. Includes step-by-step calculation of the midpoint, deviation, and the resulting equation. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation