Question:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
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When solving absolute value inequalities, break them into two linear inequalities and solve.
Updated On: Mar 7, 2025
- \( (-\infty, -2) \)
- \( (-\infty, 0) \)
- \( [-2, 6] \)
- \( (-2, \infty) \)
- \( (-2, 4) \)
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The Correct Option is C
Solution and Explanation
Given the inequality \( |x - 2| \leq 4 \), this means:
\[
-4 \leq x - 2 \leq 4
\]
Adding 2 to all sides:
\[
-2 \leq x \leq 6
\]
Thus, the interval is \( [-2, 6] \).
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