Match the equations in modulus with their respective solutions

x = 0 or x = 8

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x = \pm 1

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x = -1 or x = 4

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x=4 or x=-43

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Solution

The correct option is
$| x - 4 | = 4$
$\Rightarrow x - 4 = \pm 4$
$\Rightarrow x - 4 = 4$ or $x - 4 = - 4$
$\Rightarrow x = 8$ or $x = 0$

$| 3 x | = 3$
$\Rightarrow 3 x = \pm 3$
$\Rightarrow x = \pm \frac{3}{3}$
$\Rightarrow x = \pm 1$

$| 2 x - 3 | = 5$
$\Rightarrow 2 x - 3 = \pm 5$
$\Rightarrow 2 x - 3 = 5$ or $2 x - 3 = - 5$
$\Rightarrow 2 x = 8$ or $2 x = - 2$
$\Rightarrow x = 4$ or $x = - 1$

$| 3 x - 4 | = 8$
$\Rightarrow 3 x - 4 = \pm 8$
$\Rightarrow 3 x - 4 = 8$ or $3 x - 4 = - 8$
$\Rightarrow 3 x = 12$ or $3 x = - 4$
$\Rightarrow x = 4$ or $x = - \frac{4}{3}$

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