Question:medium
If \( |x-1| + |x-3| \leq 8 \), then the values of \( x \) lie in the interval:
If \( |x-1| + |x-3| \leq 8 \), then the values of \( x \) lie in the interval:
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Geometrically, $|x-a| + |x-b| = k$ represents the sum of distances from $x$ to $a$ and $b$. If $k$ is greater than the distance between $a$ and $b$, the solution will always be a closed interval centered at the midpoint of $a$ and $b$.
Updated On: May 2, 2026
- $(-\infty, -2]$
- $[-2, 6]$
- $(-3, 7)$
- $(-2, \infty)$
- $[6, \infty)$
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The Correct Option is B
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