Verify that, $ |-x|=|x| $ for
(i) $ x=\frac{-3}{8} $.
(ii) $ x=\frac{7}{11} $.

Given:

(i) \( x=\frac{-3}{8} \).
(ii) \( x=\frac{7}{11} \).
To do:

We have to verify that \( |-x|=|x| \). 

Solution:

We know that,

$|-x|=x$, if $x \geq 0$

$|-x|=-x$, if $x<0$

Therefore,

(i) $|-x|=|-(\frac{-3}{8})|$

$=|\frac{3}{8}|$

$=\frac{3}{8}$

$|x|=|\frac{-3}{8}|$

$=|-(\frac{3}{8})|$

$=-(-\frac{3}{8})$

$=\frac{3}{8}$

LHS $=$ RHS

Hence proved.

(ii) $|-x|=|-(\frac{7}{11})|$

$=-(-\frac{7}{11})$

$=\frac{7}{11}$

$|x|=|\frac{7}{11}|$

$=\frac{7}{11}$

LHS $=$ RHS

Hence proved.

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Updated on: 10-Oct-2022

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