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Inequalities Involving Modulus Function

If |2x-7|=|9-...

Question

If $| 2^{x} - 7 | = | 9 - 2^{x} |$ , then the value of $x$ is

A

1

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B

2

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C

3

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D

4

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Solution

The correct option is C $3$
$| 2^{x} - 7 | = | 9 - 2^{x} |$
$\Rightarrow 2^{x} - 7 = \pm (9 - 2^{x})$
$2^{x} - 7 = - (9 - 2^{x})$ is not possible.
$\Rightarrow 2^{x} - 7 = 9 - 2^{x} \Rightarrow 2^{x} = 8 = 2^{3} \Rightarrow x = 3$

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