The values of x satisfying the equation x -3-4-3- is-areA- -4B- 4C- 6D- 10

The correct options are A 4 B 4 D 10||x 3| 4|=3 Case 1:|x 3| 4=3 ⇒ |x 3|=7 ⇒ x 3=±7 ⇒ x=10 or x= 4 ∴ x= 4,10 ⋯(1) Case 2:|x 3| 4= 3 nbsp; ⇒ |x 3|=1 ⇒ x ...

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Standard XII

Mathematics

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 options are
A $- 4$
B $4$
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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Absolute Value Function

Standard XII Mathematics

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

The correct options are A −4 B 4 D 10||x−3|−4|=3 Case 1:|x−3|−4=3 ⇒|x−3|=7 ⇒x−3=±7 ⇒x=10 or x=−4 ∴x=−4,10 ⋯(1) Case 2:|x−3|−4=−3 ⇒|x−3|=1 ⇒x−3=±1 ⇒x=2,4 ⋯(2) Hence, from (1) and (2), x=−4,2,4,10

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