Write an absolute value equation with these solutions -1,6

To write an absolute value equation with solutions \( x = -1 \) and \( x = 6 \), we follow these steps:

The general form of an absolute value equation is:
\[
|x - a| = b
\]
where \( a \) is the midpoint of the two solutions, and \( b \) is the distance from the midpoint to either solution.

1. Find the midpoint of \(-1\) and \(6\):
\[
\text{Midpoint} = \frac{-1 + 6}{2} = \frac{5}{2} = 2.5
\]

2. Find the distance from the midpoint to either solution:
\[
\text{Distance} = |6 - 2.5| = 3.5
\]

Thus, the absolute value equation is:
\[
\left| x - 2.5 \right| = 3.5
\]

This equation has the solutions \( x = -1 \) and \( x = 6 \).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you solve absolute value equations?
2. What is the geometric interpretation of absolute value equations?
3. Can you write an absolute value equation with different solutions?
4. How do absolute value inequalities differ from equations?
5. How can you graph an absolute value equation?

**Tip:** When solving absolute value equations, remember to consider both the positive and negative scenarios of the expression inside the absolute value.

Learn how to write an absolute value equation with solutions -1 and 6. This step-by-step guide covers key algebraic concepts like midpoint and distance formula, suitable for students in Grades 6-8.

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