https://file.aiquickdraw.com/mathbot/file/17278219200666a2srxrt.jpg

Let's break down and solve each of the questions from the image:

1. **Evaluate \(|-4| + |4|\)**:
   - The absolute value of \(-4\) is 4, and the absolute value of 4 is also 4. So:
   \[
   |-4| + |4| = 4 + 4 = 8
   \]
   **Answer: 8**

2. **Find all numbers \(x\) satisfying \(|2x - 6| = 11\)**:
   - The equation \(|2x - 6| = 11\) implies two cases:
     1. \(2x - 6 = 11\)
        - Solve: \(2x = 17 \Rightarrow x = \frac{17}{2} = 8.5\)
     2. \(2x - 6 = -11\)
        - Solve: \(2x = -5 \Rightarrow x = -\frac{5}{2} = -2.5\)
   **Answer: \(x = 8.5\) or \(x = -2.5\)**

3. **Write \([2, 7) \cup [5, 20)\) as a single interval**:
   - The union of the intervals \([2, 7)\) and \([5, 20)\) is the interval that covers both. Since these intervals overlap between 5 and 7, their union is:
   \[
   [2, 20)
   \]
   **Answer: \([2, 20)\)**

4. **Write the following into a single interval: \((-\infty, -10] \cup (-\infty, -8]\)**:
   - The union of these intervals is the interval that extends from \(-\infty\) to the maximum point where both intervals overlap, which is \(-8\). Hence, the single interval is:
   \[
   (-\infty, -8]
   \]
   **Answer: \((-\infty, -8]\)**

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Would you like further clarification or more details on any of these steps?

Here are 5 related questions for further practice:
1. What is the solution to \(|3x - 5| = 7\)?
2. How would you evaluate \(|-10| + |3|\)?
3. Can you express \((-\infty, -5) \cup (-7, 2)\) as a single interval?
4. Find the union of the intervals \([1, 4) \cup [3, 6]\).
5. Solve \(|x + 4| = 9\) for \(x\).

**Tip:** Always remember that solving absolute value equations involves considering both the positive and negative cases of the expression inside the absolute value symbol!

Evaluate |-4| + |4|, Find all numbers x satisfying |2x - 6| = 11, Write [2, 7) ∪ [5, 20) as a single interval, Write the following into a single interval (-∞, -10] ∪ (-∞, -8]

Learn how to evaluate absolute value expressions, solve absolute value equations, and express the union of intervals in a single interval. This problem covers core algebraic concepts and set theory, suitable for students in Grades 7-10.

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