Math Problem Statement
Solution
The image asks for an absolute value equation that has the solutions and .
To write an absolute value equation for this, we follow these steps:
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The absolute value equation typically takes the form , where is the midpoint of the two solutions, and is the distance from the midpoint to either solution.
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Find the midpoint between 8 and 18:
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Find the distance from the midpoint to either solution:
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The absolute value equation is then:
This equation has the solutions and .
Would you like more details or have any further questions?
Here are five related questions you might find interesting:
- What is the general form of an absolute value equation with two solutions?
- How do you solve an absolute value equation?
- How can you graph absolute value equations like the one derived?
- What are some real-world applications of absolute value equations?
- How can the concept of absolute value be extended to complex numbers?
Tip: When solving an absolute value equation, always check for two possible solutions because the equation can equal both positive and negative values.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Equations
Formulas
|x - c| = d, where c is the midpoint of the two solutions and d is the distance from the midpoint to either solution.
Theorems
Absolute Value Property: The equation |x - c| = d has two solutions: x = c + d and x = c - d.
Suitable Grade Level
Grades 7-9