Math Problem Statement
Solution
Let's break down and solve each of the questions from the image:
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Evaluate :
- The absolute value of is 4, and the absolute value of 4 is also 4. So: Answer: 8
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Find all numbers satisfying :
- The equation implies two cases:
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- Solve:
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- Solve: Answer: or
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- The equation implies two cases:
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Write as a single interval:
- The union of the intervals and is the interval that covers both. Since these intervals overlap between 5 and 7, their union is: Answer:
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Write the following into a single interval: :
- The union of these intervals is the interval that extends from to the maximum point where both intervals overlap, which is . Hence, the single interval is: Answer:
Would you like further clarification or more details on any of these steps?
Here are 5 related questions for further practice:
- What is the solution to ?
- How would you evaluate ?
- Can you express as a single interval?
- Find the union of the intervals .
- Solve for .
Tip: Always remember that solving absolute value equations involves considering both the positive and negative cases of the expression inside the absolute value symbol!
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Math Problem Analysis
Mathematical Concepts
Absolute Value
Solving Absolute Value Equations
Set Theory
Intervals
Formulas
Absolute value formula |a| = a if a >= 0, -a if a < 0
Absolute value equation |x - a| = b implies x - a = b or x - a = -b
Theorems
Properties of absolute value
Union of intervals
Suitable Grade Level
Grades 7-10