Question

If ||x-1|-5|= 2 then the number of distinct
value of x is​

Answer 1

$Given \: \|x-1|-5| = 2$

$\implies |x-1| - 5 = \pm 2$

$\implies |x-1| = 5 \pm 2$

$\implies |x-1| = 5+ 2 \: or \: |x-1| = 5 - 2$

$\implies |x-1| = 7 \: or \: |x-1| = 3$

$\implies x-1= \pm 7 \: or \: x-1= \pm 3$

$\implies x = 1 \pm 7 \: or \: x = 1 \pm 3$

$\implies x = 1+7 \:or \: x = 1-7 \:or \: x = 1+3 \:or \: x = 1-3$

$\implies x = 8 \: or \:x = -6 \:or \: x = 4 \:Or \:x = -2$

Therefore.,

$\green {The \: number \: of \: distinct \: values}$

$\green {of \: x : -6,-2,4,8 }$

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Answer 2

Answer:

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