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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