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REFER THE PIC
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Given equation ∣∣x−1∣+a∣=4
∣x−1∣+a=±4
⇒∣x−1∣=4−a or −4−a.
∴ for real x,
4−a≥0 or −4−a≥0.
⇒a≤4 or a≤−4
Hence,(-infinity,4); (- infinity,-4); (-4,4) satisfies above inequalities
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