https://file.aiquickdraw.com/mathbot/file/172597276285773zxfreb.jpg

We are given the inequality:

\[
|x - 6| \leq 10
\]

### Step 1: Understand the Absolute Value Inequality
An absolute value inequality like \( |x - 6| \leq 10 \) means that the expression inside the absolute value, \(x - 6\), is constrained to be between \(-10\) and \(10\). This is because the absolute value of a number represents its distance from 0, so the inequality \( |x - 6| \leq 10 \) can be rewritten as:

\[
-10 \leq x - 6 \leq 10
\]

### Step 2: Solve for \(x\)
Now, to solve for \(x\), we add 6 to all parts of the inequality:

\[
-10 + 6 \leq x - 6 + 6 \leq 10 + 6
\]

Simplifying the inequality:

\[
-4 \leq x \leq 16
\]

### Step 3: Conclusion
The solution to the inequality is:

\[
-4 \leq x \leq 16
\]

Thus, the correct answer is **Option B**: \(-4 \leq x \leq 16\).

---

Would you like any further details or explanations?

Here are five related questions to practice:

1. Solve \( |x + 5| \leq 7 \).
2. Solve \( |x - 3| \geq 8 \).
3. What does \( |x - 2| < 4 \) represent on a number line?
4. How would you solve \( |x + 1| > 3 \)?
5. How does the solution change if we replace \( \leq \) with \( \geq \) in \( |x - 6| \leq 10 \)?

**Tip:** For absolute value inequalities, remember that \( |A| \leq B \) becomes \( -B \leq A \leq B \), and \( |A| \geq B \) becomes two separate cases \( A \geq B \) or \( A \leq -B \).

Solve the inequality: |x - 6| ≤ 10 for x.

Learn how to solve the absolute value inequality |x - 6| ≤ 10. This detailed solution demonstrates the process of rewriting the absolute value inequality and solving it to find the range of x. The inequality solution is -4 ≤ x ≤ 16, perfect for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation