Math Problem Statement
give 10000% correct
Solution
To solve this problem, we need to find an absolute value equation that matches the given points on the number line.
The two points shown are at and . In an absolute value equation of the form , is the midpoint of these two numbers, and is the distance from the midpoint to either of the points.
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Step 1: Find the midpoint
- The midpoint between and is: So, the midpoint is .
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Step 2: Find the distance from the midpoint
- The distance from to either or is: Therefore, the distance is 2.
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Step 3: Write the equation
- The absolute value equation that satisfies this is: (since ).
Thus, the correct answer is:
Let me know if you'd like more details or have any questions!
Here are 5 related questions:
- What is the general form of an absolute value equation?
- How do you determine the midpoint between two points?
- Can an absolute value equation have more than two solutions?
- How does shifting affect the graph of an absolute value equation?
- How do you solve an absolute value equation like ?
Tip: When working with absolute value equations, always remember the midpoint is the center of symmetry between the two solutions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Equations
Midpoints
Distance
Formulas
|x - a| = b
Midpoint formula: (x1 + x2) / 2
Theorems
Absolute Value Theorem
Suitable Grade Level
Grades 8-10