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Absolute Value Function

The values of...

Question

The value(s) of $x$ satisfying the equation $| | x - 3 | - 4 | = 3$ , is/are

- 4

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4

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6

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10

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Solution

The correct option is D $10$
$| | x - 3 | - 4 | = 3$

$Case 1 : | x - 3 | - 4 = 3$
$\Rightarrow | x - 3 | = 7$
$\Rightarrow x - 3 = \pm 7$
$\Rightarrow x = 10$ or $x = - 4$
$∴ x = - 4, 10 \dots (1)$

$Case 2 : | x - 3 | - 4 = - 3$
$\Rightarrow | x - 3 | = 1$
$\Rightarrow x - 3 = \pm 1$
$\Rightarrow x = 2, 4 \dots (2)$

Hence, from $(1)$ and $(2)$ , $x = - 4, 2, 4, 10$

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